1,167 results
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2. Asymptotic behavior of some differential inequalities with mixed delays on time scales and their applications.
- Author
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Bingxian Wang and Mei Xu
- Subjects
DIFFERENTIAL inequalities ,FIXED point theory ,DISCRETE systems ,DYNAMICAL systems - Abstract
In this paper, we investigate the asymptotic stability of the trajectories governed by some delay differential inequalities on time scales. Based on time scale theory and the fixed-point theorem, some sufficient conditions are obtained for guaranteeing asymptotic stability. It is interesting that the inequalities studied in this paper include the generalized Halanay inequalities. Due to the fact that dynamic systems on a time scale unify discrete and continuous systems, the results of this paper have wider application value. Furthermore, some numerical examples verify the main results. [ABSTRACT FROM AUTHOR]
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- 2024
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3. SOME NEW OBSERVATIONS ON w-DISTANCE AND F-CONTRACTIONS.
- Author
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Kadelburg, Zoran and Radenović, Stojan
- Subjects
CONTRACTIONS (Topology) ,METRIC spaces ,FIXED point theory - Abstract
The aim of this paper is to present some new observations about w-distance (in the sense of O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japonica 44, 2 (1996), 381-391) and F-contractions (in the sense of D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012:94 (2012)). Both concepts have been examined separately a lot, but there have been few attempts to connect them. This article is a step in filling this gap. Besides, some comments and improvements of results in the existing literature are presented. [ABSTRACT FROM AUTHOR]
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- 2024
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4. Critical remarks on “Existence of the solution to second order differential equation through fixed point results for nonlinear F-contractions involving w0-distance”.
- Author
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Kadelburg, Zoran, Fabiano, Nicola, Savatović, Milica, and Radenović, Stojan
- Subjects
DIFFERENTIAL equations ,FIXED point theory ,FUNCTIONAL analysis - Abstract
Copyright of Military Technical Courier / Vojnotehnicki Glasnik is the property of Military Technical Courier / Vojnotehnicki Glasnik and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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- 2023
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5. Existence and convergence of fixed points for noncyclic φ-contractions.
- Author
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Safari-Hafshejani, Akram
- Subjects
FIXED point theory ,BANACH spaces ,MATHEMATICS ,LAGRANGE equations ,MATHEMATICAL optimization - Abstract
In the paper, we introduce a new class of noncyclic φ-contractions as a generalization of the class of noncyclic contractions which was first introduced in the paper [R. Esp'ınola, M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numerical Functional Analysis and Optimization 34 (8), 845-860, 2013] and study the existence, uniqueness and convergence of a fixed point for such class of noncyclic mapping in the framework of uniformly convex Banach spaces. We obtain existence results of the best proximity points for cyclic φ-contractions as a consequence of our main theorems. [ABSTRACT FROM AUTHOR]
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- 2024
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6. Some Common Fixed Point Results of Tower Mappings in (Pseudo)modular Metric Spaces.
- Author
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Francis, Daniel, Okeke, Godwin Amechi, and Khan, Safeer Hussain
- Subjects
METRIC spaces ,FIXED point theory - Abstract
In this paper, we prove the existence and uniqueness of common fixed point of tower type contractive mappings in complete metric (pseudo)modular spaces involving the theoretic relation. However, the newly introduced contraction in this paper further characterize and includes in their full strength several existing results in metrical fixed point theory. Some nontrivial supportive examples were given to justify our result. Our results generalize, improve, and unify some existing results. [ABSTRACT FROM AUTHOR]
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- 2024
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7. Three-Body 3D-Kepler Electromagnetic Problem—Existence of Periodic Solutions.
- Author
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Angelov, Vasil Georgiev
- Subjects
EQUATIONS of motion ,PERIODIC functions ,FIXED point theory ,CLASSICAL electromagnetism ,UNIQUENESS (Mathematics) - Abstract
The main purpose of the present paper is to prove the existence of periodic solutions of the three-body problem in the 3D Kepler formulation. We have solved the same problem in the case when the three particles are considered in an external inertial system. We start with the three-body equations of motion, which are a subset of the equations of motion (previously derived by us) for any number of bodies. In the Minkowski space, there are 12 equations of motion. It is proved that three of them are consequences of the other nine, so their number becomes nine, as much as the unknown trajectories are. The Kepler formulation assumes that one particle (the nucleus) is placed at the coordinate origin. The motion of the other two particles is described by a neutral system with respect to the unknown velocities. The state-dependent delays arise as a consequence of the finite vacuum speed of light. We obtain the equations of motion in spherical coordinates and split them into two groups. In the first group all arguments of the unknown functions are delays. We take their solutions as initial functions. Then, the equations of motion for the remaining two particles must be solved to the right of the initial point. To prove the existence–uniqueness of a periodic solution, we choose a space consisting of periodic infinitely smooth functions satisfying some supplementary conditions. Then, we use a suitable operator which acts on these spaces and whose fixed points are periodic solutions. We apply the fixed point theorem for the operators acting on the spaces of periodic functions. In this manner, we show the stability of the He atom in the frame of classical electrodynamics. In a previous paper of ours, we proved the existence of spin functions for plane motion. Thus, we confirm the Bohr and Sommerfeld's hypothesis for the He atom. [ABSTRACT FROM AUTHOR]
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- 2024
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8. MERGING OF UNITS BASED ON INVERSE DATA ENVELOPMENT ANALYSIS.
- Author
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GHOBADI, S. and SOLEIMANI-CHAMKHORAMI, KH.
- Subjects
DATA envelopment analysis ,MATHEMATICAL models ,ARTIFICIAL neural networks ,VECTORS (Calculus) ,FIXED point theory - Abstract
Inverse data envelopment analysis (InvDEA) is a remarkable and popular management tool. This paper deals with one application of this tool. In fact, the problem of the merging of units is investigated in the presence of negative data. The problem of merging units refers to the fact that a set of units create a new unit based on synergy to improve their performance. We use multiple objective programming for this purpose and suggest new models based on predetermined conditions for new units. The proposed models estimate inputs and outputs simul- taneously. Importance advantages of the proposed models are: i) We can follow multiple goals in the problem of merging units because mul- tiple objective programming is applied. ii) Models can simultaneously estimate the inputs and outputs of the combined unit. iii) Unlike the existing methods in the InvDEA-based merging literature, the negative data do not need to be transferred to positive data. Finally, a numerical example is used to explain and validate the model proposed in this paper. [ABSTRACT FROM AUTHOR]
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- 2024
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9. Mathematical coding theory and its applications.
- Author
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Solé, Patrick
- Subjects
DISCRETE mathematics ,FIXED point theory ,NONCOMMUTATIVE rings ,GENERAL relativity (Physics) ,ALGEBRAIC coding theory - Abstract
This document is an editorial for a special issue of the journal AIMS Mathematics on "Mathematical Coding Theory and its Applications." The issue includes 8 papers that explore various aspects of coding theory, which involves techniques from commutative algebra, discrete mathematics, and the geometry of numbers. The papers cover topics such as codes over rings (including non-commutative and non-unitary rings), codes for alternative metrics, and codes as ideals in special rings. The issue also includes papers on codes over fields, including finite fields and number fields. The guest editor for the special issue is Professor Patrick Solé from the University of Aix-Marseille in France. [Extracted from the article]
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- 2024
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10. Investigation of multi-term delay fractional differential equations with integro-multipoint boundary conditions.
- Author
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Alghamdi, Najla, Ahmad, Bashir, Alharbi, Esraa Abed, and Shammakh, Wafa
- Subjects
BOUNDARY value problems ,DELAY differential equations ,FRACTIONAL differential equations ,INTEGRO-differential equations ,FIXED point theory ,INTEGRAL operators ,FRACTIONAL integrals - Abstract
A new class of nonlocal boundary value problems consisting of multi-term delay fractional differential equations and multipoint-integral boundary conditions is studied in this paper. We derive a more general form of the solution for the given problem by applying a fractional integral operator of an arbitrary order βξ instead of β1; for details, see Lemma 2.2. The given problem is converted into an equivalent fixed-point problem to apply the tools of fixed-point theory. The existence of solutions for the given problem is established through the use of a nonlinear alternative of the Leray-Schauder theorem, while the uniqueness of its solutions is shown with the aid of Banach's fixed-point theorem. We also discuss the stability criteria, icluding Ulam-Hyers, generalized Ulam-Hyers, Ulam-Hyers-Rassias, and generalized Ulam-Hyers-Rassias stability, for solutions of the problem at hand. For illustration of the abstract results, we present examples. Our results are new and useful for the discipline of multi-term fractional differential equations related to hydrodynamics. The paper concludes with some interesting observations. [ABSTRACT FROM AUTHOR]
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- 2024
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11. Abstract random differential equations with state-dependent delay using measures of noncompactness.
- Author
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Heris, Amel, Bouteffal, Zohra, Salim, Abdelkrim, Benchohra, Mouffak, and Karapınar, Erdal
- Subjects
DIFFERENTIAL equations ,EXISTENCE theorems ,GENERALIZATION ,FIXED point theory ,FRECHET spaces - Abstract
This paper is devoted to the existence of random mild solutions for a general class of second-order abstract random differential equations with state-dependent delay. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measures of noncompactness. An application related to partial random differential equations with state-dependent delay is presented. [ABSTRACT FROM AUTHOR]
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- 2024
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12. A new faster iteration process to fixed points of generalized α-nonexpansive mappings in Banach spaces.
- Author
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Rahimi, Asghar, Rezaei, Ali, Daraby, Bayaz, and Ghasemi, Mostafa
- Subjects
BANACH spaces ,APPROXIMATION theory ,DIFFERENTIABLE mappings ,MATHEMATICS theorems ,FIXED point theory - Abstract
In this paper, we introduce a new iterative scheme to approximate the fixed point of generalized α-nonexpansive mappings. we first prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized α-nonexpansive mappings. Using the example presented in [R. Pant and R. Shukla, Approximating fixed point of generalized α-nonexpansive mappings in Banach spaces, J. Numer. Funct. Anal. Optim. 38(2017) 248-266.], we compare the convergence behavior of the new iterative process with other iterative processes. [ABSTRACT FROM AUTHOR]
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- 2024
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13. Parameters optimization of three-element dynamic vibration absorber with inerter and grounded stiffness.
- Author
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Baduidana, Marcial and Kenfack-Jiotsa, Aurelien
- Subjects
VIBRATION absorbers ,FIXED point theory ,STEADY-state responses ,EQUATIONS of motion - Abstract
Improving the control performance of dynamic vibration absorbers has recently been effective by introducing a grounded negative stiffness device. However, the negative stiffness structure is unstable and difficult to achieve in engineering practice , and its major drawback is that it amplif ies the vibration response of the primary system at low frequency region. Meanwhile, some mechanical devices can be combined to make the DVA work even better with a grounded positive stiffness. For this purpose, this paper combines for the first time the control effect of the inerter device and grounded positive stiffness into a three-element DVA model in order to better improve vibration reduction of an undamped primary system under excitation. First, the dynamic equation of motion of the system is written according to Newton 's second law. Then, the steady-state displacement response of the primary system under harmonic excitation is calculated. In order to minimize the resonant response of the primary system around its natural frequency, the extended fixed point theory is applied. Thus, the optimized parameters such as the tuning frequency ratio, the stiffness ratio , and the approximate damping ratio are determined as a function of mass ratio and inerter – mass ratio. From the results analysis, it was found that the inerter – mass ratio has a better working range to guarantee the stability of the coupled system. Then , study on the effect of inerter – mass ratio on the primary system response is carried out. It can be seen that increasing the inerter – mass ratio in the optimal working range can reduce the response of the primary system beyond its uncontrolled static response. However, it is necessary to avoid the situation where the inerter – mass ratio is very large because it can lead to unrealistic optimal parameters. Finally, comparison with other DVA models is show n under harmonic and random excitation of the primary system. It is found that the proposed DVA model in this paper has high control performance and can be used in many engineering practice s. [ABSTRACT FROM AUTHOR]
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- 2024
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14. Coupled Fixed Point Theory in Subordinate Semimetric Spaces.
- Author
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Alharbi, Areej, Noorwali, Maha, and Alsulami, Hamed H.
- Subjects
FIXED point theory ,MONOTONE operators - Abstract
The aim of this paper is to study the coupled fixed point of a class of mixed monotone operators in the setting of a subordinate semimetric space. Using the symmetry between the subordinate semimetric space and a JS-space, we generalize the results of Senapati and Dey on JS-spaces. In this paper, we obtain some coupled fixed point results and support them with some examples. [ABSTRACT FROM AUTHOR]
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- 2024
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15. On Prešić-Type Mappings: Survey.
- Author
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Achtoun, Youssef, Gardasević-Filipović, Milanka, Mitrović, Slobodanka, and Radenović, Stojan
- Subjects
FIXED point theory ,FUNCTIONAL analysis ,RESEARCH personnel - Abstract
This paper is dedicated to the memory of the esteemed Serbian mathematician Slaviša B. Prešić (1933–2008). The primary aim of this survey paper is to compile articles on Prešić-type mappings published since 1965. Additionally, it introduces a novel class of symmetric contractions known as Prešić–Menger and Prešić–Ćirić–Menger contractions, thereby enriching the literature on Prešić-type mappings. The paper endeavors to furnish young researchers with a comprehensive resource in functional and nonlinear analysis. The relevance of Prešić's method, which generalizes Banach's theorem from 1922, remains significant in metric fixed point theory, as evidenced by recent publications. The overview article addresses the growing importance of Prešić's approach, coupled with new ideas, reflecting the ongoing advancements in the field. Additionally, the paper establishes the existence and uniqueness of fixed points in Menger spaces, contributing to the filling of gaps in the existing literature on Prešić's works while providing valuable insights into this specialized domain. [ABSTRACT FROM AUTHOR]
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- 2024
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16. Positive periodic solution for enterprise cluster model with feedback controls and time-varying delays on time scales.
- Author
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Peng, Chun, Li, Xiaoliang, and Du, Bo
- Subjects
TIME delay systems ,FIXED point theory ,PSYCHOLOGICAL feedback - Abstract
This paper aims to study a class of enterprise cluster models with feedback controls and time-varying delays on time scales. Based on periodic time scales theory and the fixed point theorem of strict-set-contraction, some new sufficient conditions for the existence of positive periodic solutions are obtained. Finally, two examples are presented to verify the validity and applicability of the main results in this paper. [ABSTRACT FROM AUTHOR]
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- 2024
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17. Metrization of soft metric spaces and its application to fixed point theory.
- Author
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Soylu, Gültekin and Çerçi, Müge
- Subjects
FIXED point theory ,METRIC spaces ,SOFT sets - Abstract
Soft set theory has attracted many researchers from several different branches. Sound theoretical improvements are accompanied with successful applications to practical solutions of daily life problems. However, some of the attempts of generalizing crisp concepts into soft settings end up with completely equivalent structures. This paper deals with such a case. The paper mainly presents the metrizability of the soft topology induced by a soft metric. The soft topology induced by a soft metric is known to be homeomorphic to a classical topology. In this work, it is shown that this classical topology is metrizable. Moreover, the explicit construction of an ordinary metric that induces the classical topology is given. On the other hand, it is also shown that soft metrics are actually cone metrics. Cone metrics are already proven to be an unsuccessful attempt of generalizing metrics. These results clarify that most, if not all, properties of soft metric spaces could be directly imported from the related classical theory. The paper concludes with an application of the findings, i.e., a new soft fixed point theorem is stated and proven with the help of the obtained homemorphism. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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18. Fixed point and endpoint theorems of multivalued mappings in convex $ b $-metric spaces with an application.
- Author
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Ji, Dong, Yu, Yao, and Li, Chaobo
- Subjects
SET-valued maps ,FIXED point theory ,NONLINEAR integral equations - Abstract
In this paper, we investigated several new fixed points theorems for multivalued mappings in the framework b -metric spaces. We first generalized S -iterative schemes for multivalued mappings to above spaces by means of a convex structure and then we developed the existence of fixed points and approximate endpoints of the multivalued contraction mappings using iteration techniques. Furthermore, we introduced the modified S -iteration process for approximating a common endpoint of a multivalued α s -nonexpansive mapping and a multivalued mapping satisfying conditon (E ′ ) . We also showed that this new iteration process converges faster than the S -iteration process in the sense of Berinde. Some convergence results for this iterative procedure to a common endpoint under some certain additional hypotheses were proved. As an application, we applied the S -iteration process in finding the solution to a class of nonlinear quadratic integral equations. In this paper, we investigated several new fixed points theorems for multivalued mappings in the framework -metric spaces. We first generalized -iterative schemes for multivalued mappings to above spaces by means of a convex structure and then we developed the existence of fixed points and approximate endpoints of the multivalued contraction mappings using iteration techniques. Furthermore, we introduced the modified -iteration process for approximating a common endpoint of a multivalued -nonexpansive mapping and a multivalued mapping satisfying conditon . We also showed that this new iteration process converges faster than the -iteration process in the sense of Berinde. Some convergence results for this iterative procedure to a common endpoint under some certain additional hypotheses were proved. As an application, we applied the -iteration process in finding the solution to a class of nonlinear quadratic integral equations. [ABSTRACT FROM AUTHOR]
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- 2024
- Full Text
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19. On the Solvability of Iterative Systems of Fractional-Order Differential Equations with Parameterized Integral Boundary Conditions.
- Author
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Krushna, Boddu Muralee Bala and Khuddush, Mahammad
- Subjects
DIFFERENTIAL equations ,BOUNDARY value problems ,FIXED point theory ,FRACTIONAL calculus ,MATHEMATICAL formulas - Abstract
The aim of this paper is to determine the eigenvalue intervals of μk; 1 < k < n for which an iterative systems of a class of fractional-order differential equations with parameterized integral boundary conditions (BCs) has at least one positive solution by means of standard fixed point theorem of cone type. To the best of our knowledge, this will be the first time that we attempt to reach such findings for the topic at hand in the literature. The obtained results in the paper are illustrated with an example for their feasibility. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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20. Preface to the Special Issue "Abstract Fractional Integro-Differential Equations and Fixed Point Theory with Applications".
- Author
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Du, Wei-Shih, Kostić, Marko, Fedorov, Vladimir E., and Pinto, Manuel
- Subjects
FIXED point theory ,INTEGRO-differential equations ,FRACTIONAL calculus - Abstract
This document is a preface to a special issue of the journal Mathematics, focusing on abstract fractional integro-differential equations and fixed point theory with applications. The preface explains that fractional calculus is used to model complex systems in various disciplines, and abstract fractional integro-differential equations arise from different scientific research areas. The special issue includes 12 research papers selected from 36 submissions, covering topics such as almost periodic solutions, stability analysis, and convex analysis. The authors express their appreciation to the contributors and reviewers, and hope that the papers will inspire future research in these areas. [Extracted from the article]
- Published
- 2023
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21. ON THE EXISTENCE OF SOLUTIONS TO BOUNDARY VALUE PROBLEMS ON INFINTE INTERVALS FOR NONLINEAR DISCRETE SYSTEMS.
- Author
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RODR'IGUEZ, JES 'US
- Subjects
BOUNDARY value problems ,INFINITY (Mathematics) ,SCHAUDER bases ,FIXED point theory ,LEAST fixed point (Mathematics) - Abstract
We provide criteria for the existence of solutions of nonlinear discrete-time boundary value problems on infinite-time intervals. The problems are formulated as nonlinear operator equations on sequence spaces and the tools of nonlinear functional analysis are employed throughout the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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22. Perturbed functional fractional differential equation of Caputo-Hadamard order.
- Author
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HAMANI, SAMIRA
- Subjects
FRACTIONAL differential equations ,FUNCTIONAL differential equations ,BANACH spaces ,FIXED point theory - Abstract
In this paper, we investigate the existence of solution and extremal solutions for an initial-value problem of perturbed functional fractional differential equations with Caputo-Hadamard derivative. Our analysis relies on the fixed point theorem of Burton and Kirk and the concept of upper and lower solutions combined with a fixed point theorem in ordered Banach space established by Dhage and Henderson. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Asymptotic enumeration of graphs by degree sequence, and the degree sequence of a random graph.
- Author
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Liebenau, Anita and Wormald, Nick
- Subjects
RANDOM graphs ,FIXED point theory ,MATHEMATICAL formulas ,PARAMETER estimation ,MATHEMATICAL models - Abstract
In this paper we relate a fundamental parameter of a random graph, its degree sequence, to a simple model of nearly independent binomial random variables. As a result, many interesting functions of the joint distribution of graph degrees, such as the distribution of the median degree, become amenable to estimation. Our result is established by proving an asymptotic formula conjectured in 1990 for the number of graphs with given degree sequence. In particular, this gives an asymptotic formula for the number of d-regular graphs for all d, as n→∞. The key to our results is a new approach to estimating ratios between point probabilities in the space of degree sequences of the random graph, including analysis of fixed points of the associated operators. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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24. MULTIVALUED COUPLED COINCIDENCE POINT RESULTS IN METRIC SPACES.
- Author
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Choudhury, Binayak S., Metiya, Nikhilesh, and Kundu, Sunirmal
- Subjects
FIXED point theory ,COINCIDENCE ,SET-valued maps - Abstract
In this paper, we use an inequality involving a coupled multivalued mapping and a singlevalued mapping to obtain a coupled coincidence point theorem. We discuss special conditions under which coupled common fixed point theorems are obtained. The result combines several ideas prevalent in fixed point theory studies. There are several corollaries and illustrative examples. The Hausdorff-Pompeiu metric between sets is used. The work is in the context of metric spaces and is a part of set-valued analysis with the singlevalued consequences. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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25. Some Applications Related to Differential Inclusions Based on the Use of a Weighted Space.
- Author
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İlter, Serkan
- Subjects
ORDINARY differential equations ,FIXED point theory ,DIFFERENTIAL inclusions ,MATHEMATICAL models ,MATHEMATICAL analysis - Abstract
In this paper, we present an existence theorem for the problem of discontinuous dynamical system related to ordinary differential inclusion, based on the use of the concepts related to weighted spaces introduced by G'orka and Rybka, without using any fixed point theorem. The solution concept in this theorem is considered to belong to the weighted space. For comparison with the classical case and as an application of the theorem, we give an example problem that has such a solution but no continuously differentiable solution. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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26. A theoretical view of existence results by using fixed point theory for quasi-variational inequalities.
- Author
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Min Wang, Karaca, Yeliz, ur Rahman, Mati, and Mi Zhou
- Subjects
BANACH spaces ,FIXED point theory - Abstract
In this paper, we present new existence results for the quasivariational inequality problem (QV I) in reflexive Banach spaces using the fixed point method with quasi-monotonicity and local upper sign-continuity assumptions. These results improve upon previous ones which only required a weaker monotonicity condition and did not impose compactness on the involved set. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
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27. Fractional Dynamics of Cassava Mosaic Disease Model with Recovery Rate Using New Proposed Numerical Scheme.
- Author
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Abdullah, Tariq Q. S., Huang, Gang, Al-Sadi, Wadhah, Aboelmagd, Yasser, and Mobarak, Wael
- Subjects
FIXED point theory ,MOSAIC diseases ,AGRICULTURAL pests ,PLANT viruses ,FOOD security ,CASSAVA - Abstract
Food security is a basic human right that guarantees humans an adequate amount of nutritious food. However, plant viruses and agricultural pests cause real damage to food sources, leading to negative impacts on meeting the human right of obtaining a sufficient amount of food. Understanding infectious disease dynamics can help us to design appropriate control and prevention strategies. Although cassava is among the most produced and consumed crops and greatly contributes to food security, cassava mosaic disease causes a decrease in photosynthesis and reduces cassava yield, resulting in a lack of crops. This paper developed a fractional model for cassava mosaic disease (CMD) dynamics based on the Caputo–Fabrizio (CF) fractional derivative to decrease cassava plant infection. We used fixed-point theory to study the existence of a unique solution in the form of the CMD model. A stability analysis of the model was conducted by using fixed-point theory and the Picard technique. A new numerical scheme was proposed for solving the nonlinear system of a fractional model in the sense of the CF-derivative and applied to obtain numerical simulations for a fractional model of the dynamics of CMD. The obtained results are described using figures that show the dynamics and behaviors of the compartments of CMD, and it is concluded that decreasing the population of whitefly vectors can prevent cassava plants from becoming infected better than increasing the recovery rate of the infected cassava plants. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. A robust numerical study on modified Lumpy skin disease model.
- Author
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Kumar, Parveen, Kumar, Sunil, Alkahtani, Badr Saad T., and Alzaid, Sara S.
- Subjects
LUMPY skin disease ,EXPONENTIAL decay law ,FIXED point theory ,CONSCIOUSNESS raising ,MEDICAL model - Abstract
This paper was to present a mathematical model of non-integer order and demonstrated the detrimental consequences of lumpy skin disease (LSD). The LSD model included primarily affected cattle and other animals, particularly buffalo and cows. Given the significant drop in the number of livestock and dairy products, it was essential to use mathematical models to raise awareness of this issue. We examined the suggested LSD model to understand as well as every possible avenue that could result in the illness spreading throughout the community. Ulam-Hyers stability made it easier to analyze the stability of the LSD model, and fixed-point theory was a valuable tool for finding the existence and uniqueness of the solution to the suggested model. We have used new versions of power law and exponential decay fractional numerical methods. Numerical calculations were showing the influence of various fractional orders on the spread of disease and provided more informations than integer orders for the sensitive parameters of the proposed model. The graphical depiction is showed an understanding of the proposed LSD model. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Fixed point theorems for enriched Kannan-type mappings and application.
- Author
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Yao Yu, Chaobo Li, and Dong Ji
- Subjects
VOLTERRA equations ,METRIC spaces ,CONVEX sets ,MATHEMATICS ,FIXED point theory - Abstract
The aim of this paper is to establish some fixed point results for enriched Kannan-type mappings in convex metric spaces. We first give an affirmative answer to a recent Berinde and Păcurar's question (Remark 2.3) [J. Comput. Appl. Math., 386 (2021), 113217]. Furthermore, we establish the existence and uniqueness of fixed points for Suzuki-enriched Kannan-type mappings in the setting of convex metric spaces. Finally, we present an application to approximate the solution of the Volterra integral equations to support our results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. On the solutions of a nonlinear system of q-difference equations.
- Author
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Turan, Nihan, Başarır, Metin, and Şahin, Aynur
- Subjects
NONLINEAR equations ,BOUNDARY value problems ,INITIAL value problems ,DIFFERENCE equations ,EQUATIONS - Abstract
In this paper, we examine the existence and uniqueness of solutions for a system of the first-order q-difference equations with multi-point and q-integral boundary conditions using various fixed point (fp) theorems. Also, we give two examples to support our results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. A Novel Fixed-Point Iteration Approach for Solving Troesch's Problem.
- Author
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Filali, Doaa, Ali, Faeem, Akram, Mohammad, and Dilshad, Mohammad
- Subjects
GREEN'S functions ,BOUNDARY value problems ,NONLINEAR differential equations ,FIXED point theory ,BANACH spaces - Abstract
This paper introduces a novel F fixed-point iteration method that leverages Green's function for solving the nonlinear Troesch problem in Banach spaces, which are symmetric spaces. The Troesch problem, characterized by its challenging boundary conditions and nonlinear nature, is significant in various physical and engineering applications. The proposed method integrates fixed-point theory with Green's function techniques to develop an iteration process that ensures convergence, stability, and accuracy. The numerical experiments demonstrate the method's efficiency and robustness, highlighting its potential for broader applications in solving nonlinear differential equations in Banach spaces. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Positive Radial Symmetric Solutions of Nonlinear Biharmonic Equations in an Annulus.
- Author
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Li, Yongxiang and Yang, Shengbin
- Subjects
FIXED point theory ,NONLINEAR equations ,CONTINUOUS functions ,CONES ,BIHARMONIC equations - Abstract
This paper discusses the existence of positive radial symmetric solutions of the nonlinear biharmonic equation ▵ 2 u = f (u , ▵ u) on an annular domain Ω in R N with the Navier boundary conditions u | ∂ Ω = 0 and ▵ u | ∂ Ω = 0 , where f : R + × R − → R + is a continuous function. We present some some inequality conditions of f to obtain the existence results of positive radial symmetric solutions. These inequality conditions allow f (ξ , η) to have superlinear or sublinear growth on ξ , η as | (ξ , η) | → 0 and ∞. Our discussion is mainly based on the fixed-point index theory in cones. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. Nonlinear Contractions Employing Digraphs and Comparison Functions with an Application to Singular Fractional Differential Equations.
- Author
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Filali, Doaa, Dilshad, Mohammad, and Akram, Mohammad
- Subjects
FRACTIONAL differential equations ,BOUNDARY value problems ,METRIC spaces ,FIXED point theory ,CONTRACTIONS (Topology) - Abstract
After the initiation of Jachymski's contraction principle via digraph, the area of metric fixed point theory has attracted much attention. A number of outcomes on fixed points in the context of graph metric space employing various types of contractions have been investigated. The aim of this paper is to investigate some fixed point theorems for a class of nonlinear contractions in a metric space endued with a transitive digraph. The outcomes presented herewith improve, extend and enrich several existing results. Employing our findings, we describe the existence and uniqueness of a singular fractional boundary value problem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
34. Three Existence Results in the Fixed Point Theory.
- Author
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Zaslavski, Alexander J.
- Subjects
FIXED point theory ,METRIC spaces ,SET-valued maps ,GENERALIZATION - Abstract
In the present paper, we obtain three results on the existence of a fixed point for nonexpansive mappings. Two of them are generalizations of the result for F-contraction, while third one is a generalization of a recent result for set-valued contractions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. Exploring solutions to specific class of fractional differential equations of order 3<uˆ≤4.
- Author
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Aljurbua, Saleh Fahad
- Subjects
CAPUTO fractional derivatives ,FUNCTION spaces ,FRACTIONAL differential equations ,FIXED point theory ,DIFFERENTIAL equations - Abstract
This paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order 3 < u ˆ ≤ 4 and includes a term Θ (β , Z (β)) alongside boundary conditions. Through the application of a fixed point theorem in appropriate function spaces, we consider nonlocal conditions along with necessary assumptions under which solutions to the given FDE exist. Furthermore, we offer an example to illustrate the results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. A sub-super solution method to continuous weak solutions for a semilinear elliptic boundary value problems on bounded and unbounded domains.
- Author
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Ghanmi, Abdeljabbar, Alzumi, Hadeel Z., and Zeddini, Noureddine
- Subjects
BOUNDARY value problems ,GREEN'S functions ,FIXED point theory ,NONLINEAR theories ,SEMILINEAR elliptic equations - Abstract
In this paper, we prove the existence of solutions for an elliptic system. More precisely, we combine the potential theory with the sub-super solution method and use the properties of the well-known Kato class to justify our existence results. The novelty of our study is that we consider either the bounded or the exterior domain; Also, the nonlinearities may be singular near the boundary. Some examples are presented to validate our main results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
37. Analysis of a hybrid fractional coupled system of differential equations in n-dimensional space with linear perturbation and nonlinear boundary conditions.
- Author
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Noor, Salma, Ullah, Aman, Ali, Anwar, and Aldosary, Saud Fahad
- Subjects
DIFFERENTIAL equations ,VECTOR spaces ,HYBRID systems ,FIXED point theory ,FRACTIONAL differential equations ,EXISTENCE theorems - Abstract
In this paper, we investigated n-dimensional fractional hybrid differential equations (FHDEs) with nonlinear boundary conditions in a nonlinear coupled system. For this purpose, we used Dhage's fixed point theory, and applied the Krasnoselskii-type coupled fixed point theorem to construct existence conditions of the solution of the FHDEs. To illustrated this idea, suitable examples are presented in 3-dimensional space at the end of the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. Fixed point theorems for b-generalized contractive mappings with weak continuity conditions.
- Author
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Yan Han, Shaoyuan Xu, Jin Chen, and Huijuan Yang
- Subjects
BANACH algebras ,BANACH spaces ,FIXED point theory ,METRIC spaces - Abstract
The purpose of this paper was to introduce several b-generalized contractive mappings in the framework of cone b-metric spaces over Banach algebras. The obtained contractions generalized and extended the counterparts in metric spaces, cone metric spaces, and b-metric spaces. Moreover, via weakening the completeness of the spaces, we gave some fixed point theorems for asymptotically regular mappings without considering the orbital continuity and k-continuity of the mappings. Those who need a specification is our results do not rely on the continuity of b-metric and the normality of cones. In addition, some nontrivial examples were presented to illustrate the superiority of our fixed point theorems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Fixed Point Theory in Bicomplex Metric Spaces: A New Framework with Applications.
- Author
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Alamri, Badriah
- Subjects
METRIC spaces ,CONTRACTIONS (Topology) ,FIXED point theory ,INTEGRAL equations ,VOLTERRA equations - Abstract
This paper investigates the existence of common fixed points for mappings satisfying generalized rational type contractive conditions in the framework of bicomplex valued metric spaces. Our findings extend well-established results in the existing literature. As an application of our leading result, we explore the existence and uniqueness of solutions of the Volttera integral equation of the second kind. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. Common Attractors for Generalized F -Iterated Function Systems in G -Metric Spaces.
- Author
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Nazir, Talat and Silvestrov, Sergei
- Subjects
FIXED point theory ,METRIC spaces - Abstract
In this paper, we study the generalized F-iterated function system in G-metric space. Several results of common attractors of generalized iterated function systems obtained by using generalized F-Hutchinson operators are also established. We prove that the triplet of F-Hutchinson operators defined for a finite number of general contractive mappings on a complete G-metric space is itself a generalized F-contraction mapping on a space of compact sets. We also present several examples in 2-D and 3-D for our results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. Investigation of Well-Posedness for a Direct Problem for a Nonlinear Fractional Diffusion Equation and an Inverse Problem.
- Author
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Arıbaş, Özge, Gölgeleyen, İsmet, and Yıldız, Mustafa
- Subjects
BURGERS' equation ,NONLINEAR equations ,GRONWALL inequalities ,CAPUTO fractional derivatives ,EIGENFUNCTION expansions ,INVERSE problems ,ELLIPTIC operators - Abstract
In this paper, we consider a direct problem and an inverse problem involving a nonlinear fractional diffusion equation, which can be applied to many physical situations. The equation contains a Caputo fractional derivative, a symmetric uniformly elliptic operator and a source term consisting of the sum of two terms, one of which is linear and the other is nonlinear. The well-posedness of the direct problem is examined and the results are used to investigate the stability of an inverse problem of determining a function in the linear part of the source. The main tools in our study are the generalized eigenfunction expansions theory for nonlinear fractional diffusion equations, contraction mapping, Young's convolution and generalized Grönwall's inequalities. We present a stability estimate for the solution of the inverse source problem by means of observation data at a given point in the domain. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. A Singular Tempered Sub-Diffusion Fractional Model Involving a Non-Symmetrically Quasi-Homogeneous Operator.
- Author
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Zhang, Xinguang, Chen, Peng, Li, Lishuang, and Wu, Yonghong
- Subjects
FIXED point theory ,NONLINEAR operators - Abstract
In this paper, we focus on the existence of positive solutions for a singular tempered sub-diffusion fractional model involving a quasi-homogeneous nonlinear operator. By using the spectrum theory and computing the fixed point index, some new sufficient conditions for the existence of positive solutions are derived. It is worth pointing out that the nonlinearity of the equation contains a tempered fractional sub-diffusion term, and is allowed to possess strong singularities in time and space variables. In particular, the quasi-homogeneous operator is a nonlinear and non-symmetrical operator. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. ITERATIVE SCHEMES FOR SOLVING GENERAL VARIATIONAL INEQUALITIES.
- Author
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NOOR, MUHAMMAD ASLAM and NOOR, KHALIDA INAYAT
- Subjects
VARIATIONAL inequalities (Mathematics) ,ITERATIVE methods (Mathematics) ,FIXED point theory ,STOCHASTIC convergence ,FINITE differences - Abstract
In this paper, we consider a new class of variational inequalities involving two operators, which is called the general variational inequality. We have shown that the general variational inequalities are equivalent to the fixed point problem using the projection technique. This equivalent fixed point formulation is used to discuss the existence of solution as well as to investigate several iterative methods for solving general variational inequalities. Some applications of the associated dynamical system coupled with finite difference are explored. Convergence analysis of the proposed methods is considered under suitable conditions. Since general variational inequalities include the variational inequalities, complementarity problems and nonlinear equations as special cases, our results continued to hold for these problems. The techniques and ideas of this paper be starting point for the future research. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. APPROXIMATION OF TWO GENERAL FUNCTIONAL EQUATIONS IN 2-BANACH SPACES.
- Author
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CHOONKIL PARK, NAJATI, ABBAS, MOGHIMI, MOHAMMAD B., and NOORI, BATOOL
- Subjects
BANACH spaces ,APPROXIMATION theory ,FUNCTIONAL equations ,FIXED point theory ,MATHEMATICAL functions - Abstract
In this paper, we study the Ulam stability and hyperstability of two general functional equations in several variables in 2-Banach spaces. Multi-additive and multi-Jensen functions are particular cases of these functional equations. We also improve the main results of Theorem 3 and Theorem 4 of [Ciepli'nski, K. Ulam stability of functional equations in 2-Banach spaces via the fixed point method. J. Fixed Point Theory Appl. 23 (2021), no. 3, Paper No. 33, 14 pp.] and their consequences. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. On a generalization of a relatively nonexpansive mapping and best proximity pair.
- Author
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Chaira, Karim and Seddoug, Belkassem
- Subjects
NONEXPANSIVE mappings ,FIXED point theory ,NORMED rings ,FUNCTIONAL equations ,COMMERCIAL space ventures ,GENERALIZATION - Abstract
Let A and B be two nonempty subsets of a normed space X, and let T : A ∪ B → A ∪ B be a cyclic (resp., noncyclic) mapping. The objective of this paper is to establish weak conditions on T that ensure its relative nonexpansiveness. The idea is to recover the results mentioned in two papers by Matkowski (Banach J. Math. Anal. 2:237–244, 2007; J. Fixed Point Theory Appl. 24:70, 2022), by replacing the nonexpansive mapping f : C → C with a cyclic (resp., noncyclic) relatively nonexpansive mapping to obtain the best proximity pair. Additionally, we provide an application to a functional equation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. Dynamical Transmission and Mathematical Analysis of Ebola Virus Using a Constant Proportional Operator with a Power Law Kernel.
- Author
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Xu, Changjin and Farman, Muhammad
- Subjects
EBOLA virus ,MATHEMATICAL analysis ,FIXED point theory ,FRACTIONAL differential equations ,POWER law (Mathematics) ,DECOMPOSITION method - Abstract
The Ebola virus continues to be the world's biggest cause of mortality, especially in developing countries, despite the availability of safe and effective immunization. In this paper, we construct a fractional-order Ebola virus model to check the dynamical transmission of the disease as it is impacted by immunization, learning, prompt identification, sanitation regulations, isolation, and mobility limitations with a constant proportional Caputo (CPC) operator. The existence and uniqueness of the proposed model's solutions are discussed using the results of fixed-point theory. The stability results for the fractional model are presented using Ulam–Hyers stability principles. This paper assesses the hybrid fractional operator by applying methods to invert proportional Caputo operators, calculate CPC eigenfunctions, and simulate fractional differential equations computationally. The Laplace–Adomian decomposition method is used to simulate a set of fractional differential equations. A sustainable and unique approach is applied to build numerical and analytic solutions to the model that closely satisfy the theoretical approach to the problem. The tools in this model appear to be fairly powerful, capable of generating the theoretical conditions predicted by the Ebola virus model. The analysis-based research given here will aid future analysis and the development of a control strategy to counteract the impact of the Ebola virus in a community. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
47. Piecewise pseudo almost periodic solutions of interval general BAM neural networks with mixed time-varying delays and impulsive perturbations.
- Author
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Yanshou Dong, Junfang Zhao, Xu Miao, and Ming Kang
- Subjects
TIME-varying networks ,DIFFERENTIAL inequalities ,FIXED point theory ,LINEAR matrix inequalities ,LINEAR differential equations ,EXPONENTIAL dichotomy ,EXPONENTIAL stability - Abstract
This paper is concerned with piecewise pseudo almost periodic solutions of a class of interval general BAM neural networks with mixed time-varying delays and impulsive perturbations. By adopting the exponential dichotomy of linear differential equations and the fixed point theory of contraction mapping. The sufficient conditions for the existence of piecewise pseudo almost periodic solutions of the interval general BAM neural networks with mixed time-varying delays and impulsive perturbations are obtained. By adopting differential inequality techniques and mathematical methods of induction, the global exponential stability for the piecewise pseudo almost periodic solutions of the interval general BAM neural networks with mixed time-varying delays and impulsive perturbations is discussed. An example is given to illustrate the effectiveness of the results obtained in the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. NEW IMPULSIVE-INTEGRAL INEQUALITY FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH POISSON JUMPS AND CAPUTO FRACTIONAL DERIVATIVE.
- Author
-
DONGDONG GAO and JIANLI LI
- Subjects
STOCHASTIC differential equations ,INTEGRAL inequalities ,UNIQUENESS (Mathematics) ,FIXED point theory ,MATHEMATICAL models - Abstract
In this paper, we study the existence and exponential stability in pth moment of mild solutions for a class of impulsive fractional stochastic differential equations driven by Poisson jumps. Firstly, we discuss the existence and uniqueness of mild solutions for the considered equations by the Banach fixed point theorem. Next, we establish a new impulsive-integral inequality that can effectively improve some previous results [4, 17, 5, 3, 6]. Then, we obtain the exponential stability in the pth moment of mild solutions for the considered equations with the aid of the new inequality. Finally, an example is given to illustrate the efficiency of the obtained theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. Global Stability of Fractional Order HIV/AIDS Epidemic Model under Caputo Operator and Its Computational Modeling.
- Author
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Ahmad, Ashfaq, Ali, Rashid, Ahmad, Ijaz, Awwad, Fuad A., and Ismail, Emad A. A.
- Subjects
HIV ,AIDS ,COMPUTATIONAL neuroscience ,FIXED point theory ,ORDINARY differential equations ,DIFFERENTIAL operators ,EPIDEMICS - Abstract
The human immunodeficiency virus (HIV) causes acquired immunodeficiency syndrome (AIDS), which is a chronic and sometimes fatal illness. HIV reduces an individual's capability against infection and illness by demolishing his or her immunity. This paper presents a new model that governs the dynamical behavior of HIV/AIDS by integrating new compartments, i.e., the treatment class T. The steady-state solutions of the model are investigated, and accordingly, the threshold quantity R 0 is calculated, which describes the global dynamics of the proposed model. It is proved that for R 0 less than one, the infection-free state of the model is globally asymptotically stable. However, as the threshold number increases by one, the endemic equilibrium becomes globally asymptotically stable, and in such case, the disease-free state is unstable. At the end of the paper, the analytic conclusions obtained from the analysis of the ordinary differential equation (ODE) model are supported through numerical simulations. The paper also addresses a comprehensive analysis of a fractional-order HIV model utilizing the Caputo fractional differential operator. The model's qualitative analysis is investigated, and computational modeling is used to examine the system's long-term behavior. The existence/uniqueness of the solution to the model is determined by applying some results from the fixed points of the theory. The stability results for the system are established by incorporating the Ulam–Hyers method. For numerical treatment and simulations, we apply Newton's polynomial and the Toufik–Atangana numerical method. Results demonstrate the effectiveness of the fractional-order approach in capturing the dynamics of the HIV/AIDS epidemic and provide valuable insights for designing effective control strategies. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. COMMON FIXED POINT THEOREMS IN S-METRIC SPACES INVOLVING CONTROL FUNCTION.
- Author
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Saluja, Gurucharan Singh
- Subjects
FIXED point theory ,CARTOGRAPHY ,FUNCTION algebras ,METRIC spaces ,AUTOMATIC control systems - Abstract
In this paper, we prove some common fixed point theorems in S-metric spaces for a pair of weakly compatible self-mappings using control function and give some consequences of the established result. We also furnish some examples to demonstrate the validity of the results. The results presented in this paper generalize, extend and enrich several results in the existing literature. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
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