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In 2020, Olia et al. [Olia, Z. E. D. D., Gordji, M. E. and Bagha, D. E. (2020). Banach fixed point theorem on orthogonal cone metric spaces. FACTA Universitatis (NIS) Ser. Math. Inform, 35, 1239-1250] examined orthogonal cone metric spaces. They assumed that P is a normal cone with normal constant K and that self mapping T is orthogonal continuous on the orthogonal cone metric space X in their study. This study now presentes certain required definitions on orthogonal cone metric spaces that were not previously given in [9]. The examples that show the link between existing and new definitions have also been included. The results are also generalized by eliminating the normalcy condition and utilizing point orthogonal continuity instead of general orthogonal continuity in the major results of [9]. The fundamental finding of the study is then generalized by removing the requirement of orthogonal continuity and introducing normality. In addition, certain outcomes of stated theorems are proven, and some examples are provided to demonstrate these theorems. [ABSTRACT FROM AUTHOR]

Very recently Jain et al. (J. Inequal. Appl. 2022:73, 2022) introduced the concept of multivalued F-contraction with altering distance function and investigated the existence of best proximity points for this class of mappings. In this article we prove that the existence of best proximity points for multivalued F-contraction non-self mappings can be obtained from the corresponding fixed point result for multivalued F-contraction self mappings, and so the main conclusion due to Jain et al. is not a real generalization of fixed point theory. [ABSTRACT FROM AUTHOR]

Recently, Altun et al. [1] introduced the notion of p-proximal contractions and discussed about best proximity point results for this class of mappings. Then Gabeleh and Markin [4] showed that the best proximity point theorem proved by Altun et al. in [1] follows from the fixed point theory. In this short note, we show that if the p-proximal contraction constant k < 1 3 then the existence of best proximity point for p-proximal contractions follows from the celebrated Banach contraction principle. [ABSTRACT FROM AUTHOR]

Very recently I. Beg et al. [I. Beg, A. Bartwal, S. Rawat and R.C. Dimri, Best proximity points in noncommutative Banach spaces, Comp. Appl. Math., 41, 41 (2022)] introduced the concepts of k-ordered proximal contraction of the first kind and k-ordered proximal contraction of the second kind for non-self mappings and investigated the existence of best proximity points for these two classes of mappings. In the current paper, we show that their existence results are straightforward consequences of the same conclusions in fixed point theory. [ABSTRACT FROM AUTHOR]

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]

We obtain results on the existence and approximation of fixed points of enriched contractions in quasi-Banach spaces and thus extend the previous results for enriched contractions defined on Banach spaces [Berinde, V.; Păcurar, M. Approximating fixed points of enriched contractions in Banach spaces. J. Fixed Point Theory Appl. 22 (2020), no. 2, Paper No. 38, 10 pp.]. The theoretical results are illustrated by means of an appropriate example of enriched contraction on a quasi-Banach space which is not a Banach space and thus show that our new results are effective generalizations of the previous ones in literature. [ABSTRACT FROM AUTHOR]

The paper investigates a new type of contraction called (M, K, ψ)-HR-Ćirić-Reich-Rus contractions, which extends the existing research on Ćirić-Reich-Rus contraction mappings. We prove fixed point theorems by enriching (M, K, ψ)-HR-Ćirić-Reich-Rus contractions with respect to the asymptotic regularity of generalized averaged mappings. These mappings are denoted as Tφ = (1 - φ) I + φT, where I is the identity map and φ is a function from a normed space to real numbers. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize the results on expansive mappings of Yesilkaya and Aydin from Fixed Point Results of Expansive Mappings in Metric Spaces [see Yesilkaya, S. S.; Aydin, C. Fixed Point Results of Expansive Mappings in Metric Spaces. Mathematics 8 (2020), 1800]. In the present paper we show that the conditions imposed on the function 9 can be relaxed. Thus, we present more general fixed point results for q-expansive mappings in metric spaces and prove some fixed point theorems for this class of mappings, via a different approach. Finally, we present some examples to support the new results. [ABSTRACT FROM AUTHOR]

In this paper, we develop some new multiple fixed point theorems for the sum of two operators T + S where I - T is Lipschitz invertible and S is a k-set contraction on translate of a cone in a Banach space. New existence criteria for multiple positive solutions of a singular generalized Sturm-Liouville multipoint boundary value problem are established. The article ends with an illustrative example. [ABSTRACT FROM AUTHOR]

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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This document is a retraction notice published in the Proceedings of the American Mathematical Society. The author, Khadime Salame, apologizes to the mathematical community and withdraws three papers related to fixed point theory. The papers attempted to address the question of whether left amenable semitopological semigroups have a certain fixed point property, but each paper contains errors. The author acknowledges these errors and suggests that Lau's conjecture should be regarded as an open question. The author hopes that this question will be resolved in the future. [Extracted from the article]

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]

In this paper we consider second order iterative boundary value problem with Sturm Liouville type boundary conditions and establish the existence of countably many positive symmetric solutions by using Krasnoselskii's fixed point theorem for operator on a cone. [ABSTRACT FROM AUTHOR]

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]

This paper investigates the existence of positive solutions for an iterative system of nonlinear two‐point tempered fractional boundary value problem. Utilizing Krasnoselskii's fixed point theorem in a cone, we establish criteria for the existence of positive solutions. The proofs involve transforming the problem into an equivalent Fredholm integral equation of the second kind. We further explore solution uniqueness using Rus's theorem and examine Hyers–Ulam stability, particularly for the case when only a single fractional differential equation is considered, (m = 1). Our study represents a significant departure from previous works by including Riemann–Liouville tempered fractional derivative operators and an iterative equation. This research sheds light on the diverse applications of iterative functional differential equations, extending beyond noniterative counterparts. Throughout the paper, presumptive conditions are applied, and the results are validated through illustrative examples. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

This paper deals with the problem of process faults in the Lorenz system that can affect any of the system parameters and cause the system to exhibit various behaviors. In this paper, the homoclinic orbits in the Lorenz system are described and then the occurrence of process faults in the system is investigated that can cause a homoclinic explosion, bifurcation, change of fixed point, or even instability in the system. In such systems, where a small change in one of the parameters causes large changes in the behavior of the system, to prevent disaster in industrial systems and also to stop the propagation of faults in the system, the faults must be identified as soon as possible. In this paper, the states in the system are estimated by using a reduced-order observer, and the faults are detected. The purpose of this article is to recognize the change in behavior of this system in the face of this type of fault and to express the importance of timely detection and identification of faults in the system so as not to lead to failure and disaster in industrial systems. Finally, the effect of process fault, disturbance, and sensor fault are investigated simultaneously and the states and faults in the system are estimated. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

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]

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]

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]

In this paper, we present a new approach to check the existence of best proximity points for R‐proximal contractions in the framework of metric spaces equipped with a w0‐distance and present elementary proofs of recent results by using the corresponding fixed point problems without the continuity assumption of the considered self‐mapping. We also discuss on cyclic Geraghty contractions and resolve the problem of the existence and convergence of the best proximity point for such a class of mappings. [ABSTRACT FROM AUTHOR]

The objective of the paper is to present some fixed point results verifying a relational contraction utilizing certain shifting distance functions and via a generalized class of transitive relations. Our outcomes sharpen, extend, modify, and enrich many well‐known results. To demonstrate the utility of our results, several examples are provided. We employed our results finding out a unique solution of second‐order ordinary differential equations prescribed with specific boundary conditions. [ABSTRACT FROM AUTHOR]

Most of the countries in the world are affected by the coronavirus epidemic that put people in danger, with many infected cases and deaths. The crowding factor plays a significant role in the transmission of coronavirus disease. On the other hand, the vaccines of the covid-19 played a decisive role in the control of coronavirus infection. In this paper, a fractional order epidemic model (SIVR) of coronavirus disease is proposed by considering the effects of crowding and vaccination because the transmission of this infection is highly influenced by these two factors. The nonlinear incidence rate with the inclusion of these effects is a better approach to understand and analyse the dynamics of the model. The positivity and boundedness of the fractional order model is ensured by applying some standard results of Mittag Leffler function and Laplace transformation. The equilibrium points are described analytically. The existence and uniqueness of the non-integer order model is also confirmed by using results of the fixed-point theory. Stability analysis is carried out for the system at both the steady states by using Jacobian matrix theory, Routh–Hurwitz criterion and Volterra-type Lyapunov functions. Basic reproductive number is calculated by using next generation matrix. It is verified that disease-free equilibrium is locally asymptotically stable if R 0 < 1 and endemic equilibrium is locally asymptotically stable if R 0 > 1 . Moreover, the disease-free equilibrium is globally asymptotically stable if R 0 < 1 and endemic equilibrium is globally asymptotically stable if R 0 > 1 . The non-standard finite difference (NSFD) scheme is developed to approximate the solutions of the system. The simulated graphs are presented to show the key features of the NSFD approach. It is proved that non-standard finite difference approach preserves the positivity and boundedness properties of model. The simulated graphs show that the implementation of control strategies reduced the infected population and increase the recovered population. The impact of fractional order parameter α is described by the graphical templates. The future trends of the virus transmission are predicted under some control measures. The current work will be a value addition in the literature. The article is closed by some useful concluding remarks. [ABSTRACT FROM AUTHOR]

In a famous article published in 1975, Kramosil and Michálek introduced a notion of fuzzy metric that was the origin of numerous researches and publications in several frameworks and fields. In 2010, Chistyakov introduced and discussed in detail the concept of modular metric. Since then, some authors have investigated the problem of establishing connections between the notions of fuzzy metric and modular metric, obtaining positive partial solutions. In this paper, we are interested in determining the precise relationship between these two concepts. To achieve this goal, we examine a proof, based on the use of uniformities, of the important result that the topology induced by a fuzzy metric is metrizable. As a consequence of that analysis, we introduce the notion of a weak fuzzy metric and show that every weak fuzzy metric, with continuous t-norm the minimum t-norm, generates a modular metric and, conversely, we show that every modular metric generates a weak fuzzy metric, with continuous t-norm the product t-norm. It follows that every modular metric can be generated from a suitable weak fuzzy metric, and that several examples and properties of modular metrics can be directly deduced from those previously obtained in the field of fuzzy metrics. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of solutions for a coupled system of Hilfer-Hadamard sequential fractional differential equations with multi-point Riemann-Liouville fractional integral boundary conditions via standard fixed point theorems. The existence of solutions is proved using Krasnoselskii’s fixed point theorem, while the existence and uniqueness of solutions is established using the Banach fixed point theorem. We also discuss the stability of the problem in terms of Ulam-Hyers, Ulam-Hyers-Rassias, generalized Ulam-Hyers, and generalized Ulam-Hyers-Rassias stability. As an application, some examples are presented to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to analyze the solvability of a class of stochastic functional integral equations by utilizing the measure of non-compactness with Petryshyn’s fixed point theorem in a Banach space. The results obtained in this paper cover numerous existing results concluded under some weaker conditions by many authors. An example is given to support our main theorem. [ABSTRACT FROM AUTHOR]

The computational study of fixed-point problems in distance spaces is an active and important research area. The purpose of this paper is to construct a new iterative scheme in the setting of Banach space for approximating solutions of fixed-point problems. We first prove the strong convergence of the scheme for a general class of contractions under some appropriate assumptions on the domain and a parameter involved in our scheme. We then study the qualitative aspects of our scheme, such as the stability and order of convergence for the scheme. Some nonlinear problems are then considered and solved numerically by our new iterative scheme. The numerical simulations and graphical visualizations prove the high accuracy and stability of the new fixed-point scheme. Eventually, we solve a 2D nonlinear Volterra Integral Equation (VIE) via the application of our main outcome. Our results improve many related results in fixed-point iteration theory. [ABSTRACT FROM AUTHOR]

The results in this paper are related to the existence of solutions to hybrid and non-hybrid discrete fractional three-point boundary value inclusion problems for the elastic beam equation. The development of our results is attributed to the use of the Caputo and difference operators. The existence results for the non-hybrid discrete fractional inclusion problem are established by using fixed point theory for multi-valued upper semi-continuous maps, and the case of the hybrid discrete fractional inclusion problem is treated by Dhage's fixed point theory. Additionally, we present two examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

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]

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]

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]

The convexity of space is essential in nonlinear analysis, variational inequalities and optimization theory because it guarantees the existence and uniqueness of solutions to a certain extent. Because of its wide variety of applications, mathematicians have extensively promoted and researched convexity. This paper reviews some representative convexity structures and discusses their relations from their definitions, unifying them in the abstract convex structure. Moreover, applications of main convexity structures including KKM theory and fixed point theory will be reviewed. [ABSTRACT FROM AUTHOR]

In this paper, we investigate new fixed point theorems for generalized Meir–Keeler type nonlinear mappings satisfying the condition (DH). As applications, we obtain many new fixed point theorems which generalize and improve several results available in the corresponding literature. An example is provided to illustrate and support our main results. [ABSTRACT FROM AUTHOR]

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]

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]

In this paper, we obtain a generalization of a recent result of Tam (2018) which is for iterates of a set-valued paracontracting operators in a finite-dimensional space. Our result in this paper is obtained for operators in a metric space such that every its bounded and closed set is compact. We establish a convergence of inexact iterates of the set-valued operator by taking into account computational errors. [ABSTRACT FROM AUTHOR]

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]

This paper aims to establish some fixed point results for a new class of contractive type mappings in fuzzy metric-like spaces. The results of this paper generalize and extend the Banach contraction principle and some other known results in the setting of fuzzy metric-like spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a regularized iterative scheme for solving the split common fixed point problem of asymptotically demicontractive and demimetric mappings in real Banach spaces. We then prove that the iterative scheme converges strongly to a solution to the problem, which is also a solution to a variational inequality problem. A split feasibility problem is also considered with the aid of our scheme. [ABSTRACT FROM AUTHOR]