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Abstract 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.

Very recently, P. Saha et al. [A global optimality result in probabilistic spaces using control function. Optimization. 2021;70:2387–2400] studied the existence of best proximity points for Banach type ϕ-proximal contractions in the framework of Menger probabilistic metric spaces. In this paper, we present a simple proof of their main existence result which is based on a fixed point theorem for ϕ-contractive self-mappings in complete Menger PM-spaces due to B.S. Choudhury and K. Das [A new contraction principle in Menger spaces. Acta Math Sin. 2008;24:13791386]. [ABSTRACT FROM AUTHOR]

In a recent paper [I. Altun and A. Tasdemir, On best proximity points of interpolative proximal contractions, Quaestiones Math. (2020), DOI: ] the authors proved two best proximity point theorems for a new class of non-self mappings, called interpolative Reich-Rus-Ćirić type proximal contractions of the first and second kinds. Our purpose is to show that their results follow from a fixed point theorem for interpolative Reich-Rus-Ćirić type contraction mappings [E. Karapinar, R. Agarwal and H. Aydi, Interpolative Reich-Rus-Ćirić contractions on partial metric spaces, Mathematics 6 (2018), 7 pages]. [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]

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.)

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 introduce a new class of metric spaces called the Menger probabilistic bipolar metric space and define some other notions related to this space. Moreover, we prove some uniqueness fixed point theorems for two cases including the covariant and contravariant maps. These fixed point theorems are new versions of the Banach contraction principle, Kannan theorem, and Reich-type theorem in the context of the Menger probabilistic bipolar metric space. Throughout the paper, we provide some examples to understand the definitions in the better manner. Finally, two applications are given for proving the uniqueness result in the form of an integral equation and a fractional boundary value problem. [ABSTRACT FROM AUTHOR]

This paper is primarily dedicated to investigating the existence of solutions for an impulsive fractional neutral pantograph integro-differential system (IFNPIDS) through the utilization of the Caputo-Fabrizio (CF) operator. We introduce a novel solution for our addressing system and employ fixed-point techniques to establish innovative results. The paper concludes by presenting two numerical examples, illustrating the practical applicability of our theoretical findings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to exhibit a novel two-step iterative algorithm named PV algorithm to determine the fixed points of weak contractions in Banach spaces. Data dependence result is also obtained. It is proved that this PV iterative algorithm converges strongly to the fixed point of weak contractions. This iteration is almost stable for weak contraction. Furthermore, it is proved that rate of convergence of the PV iterative algorithm is faster than Picard, Ishikawa, Mann, S,normal-S, Varat, and F* algorithms. Examples are also given to support the main result. The results of this paper are original and will further enrich the existing literature. [ABSTRACT FROM AUTHOR]

In the present paper, under certain assumptions, we establish the convergence of iterates for self-mappings of complete metric spaces with graphs which are of a contractive type. The class of mappings considered in the paper contains the so-called cyclical mappings introduced by W. A. Kirk, P. S. Srinivasan and P. Veeramani in 2003 and the class of monotone nonexpansive operators. Our results hold in the case of a symmetric graph. [ABSTRACT FROM AUTHOR]

This paper delves into fixed point findings within a complete partially ordered b-metric space, focusing on mappings that adhere to weakly contractive conditions in the presence of essential topological characteristics. These findings represent modifications of established results and further extend analogous outcomes in the existing literature. The conclusions are substantiated by illustrative examples that strengthen the conclusion of the paper. [ABSTRACT FROM AUTHOR]

This paper deals with the research of solutions of bounded variation (BV) to evolution inclusion coupled with a time and state dependent maximal monotone operator. Different problems are studied: existence of solutions, unicity of the solution, existence of periodic and bounded variation right continuous (BVRC) solutions. Second-order evolution inclusions and fractional (Caputo and Riemann–Liouville) differential inclusions are also considered. A result of the Skorohod problem driven by a time- and space-dependent operator under rough signal and a Volterra integral perturbation in the BRC setting is given. The paper finishes with some results for fractional differential inclusions under rough signals and Young integrals. Many of the given results are novel. [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 consider function , (where , , ) on three fields: the set of real, -adic and complex numbers. We study dynamical systems generated by this function on each field separately and give some comparison remarks. For real variable case we show that the real dynamical system of the function depends on the parameters . Namely, we classify the parameters to three sets and prove that: for the parameters from first class each point, for which the trajectory is well defined, is a periodic point of ; for the parameters from second class any trajectory (under ) converges to one of fixed points (there may be up to two fixed points); for the parameters from third class any trajectory is dense in . For the -adic variable we give a review of known results about dynamical systems of function . Then using a recently developed method we give simple new proofs of these results and prove some new ones related to trajectories which do not converge. For the complex variables we give a review of known results. [ABSTRACT FROM AUTHOR]

This paper aims to provide a comprehensive analysis of the advancements made in understanding Iterative Fixed-Point Schemes, which builds upon the concept of digital contraction mappings. Additionally, we introduce the notion of an Iterative Fixed-Point Schemes in digital metric spaces. In this study, we extend the idea of Iteration process Mann, Ishikawa, Agarwal, and Thakur based on the ϝ-Stable Iterative Scheme in digital metric space. We also design some fractal images, which frame the compression of Fixed-Point Iterative Schemes and contractive mappings. Furthermore, we present a concrete example that exemplifies the motivation behind our investigations. Moreover, we provide an application of the proposed Fractal image and Sierpinski triangle that compress the works by storing images as a collection of digital contractions, which addresses the issue of storing images with less storage memory in this paper. [ABSTRACT FROM AUTHOR]

The rationale of this work is to introduce the notion of graphical symmetric spaces and some fixed-point results are proved for H - (ϑ , φ) -contractions in this setting. The idea of graphical symmetric spaces generalizes various spaces equipped with a function which characterizes the distance between two points of the space. Some topological properties of graphical symmetric spaces are discussed. Some fixed-point results for the mappings defined on graphical symmetric spaces are proved. The fixed-point results of this paper generalize and extend several fixed-point results in this new setting. The main results of this paper are applied to obtain the positive solutions of fractional periodic boundary value problems. [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 was concerned with the existence and uniqueness results for a coupled system of nonlinear generalized fractional differential equations supplemented with a new class of nonlocal coupled multipoint boundary conditions containing Riemann-Stieltjes and generalized fractional integrals. The nonlinearities in the given system depend on the unknown functions as well as their lower order generalized fractional derivatives. We made use of the Leray-Schauder alternative and Banach contraction mapping principle to obtain the desired results. An illustrative example was also discussed. The paper concluded with some interesting observations. [ABSTRACT FROM AUTHOR]

In this paper, we recover some traditional results in the geometry of probability distributions, and in particular the convergence of the alternating minimisation procedure, without actually referring to probability distributions. We will do this by discussing a new general concept of two types of points: admissible and agreeable, inspired by multi–agent uncertain reasoning and belief merging. On the one hand, this presents a unique opportunity to make traditional results accessible to a wider audience as no prior knowledge of the topic is required. On the other hand, it allows us to contemplate how a group of rational agents would seek an agreement given their beliefs without necessarily expressing it in terms of probability distributions, focusing instead on logical properties. Finally, we recover Euclidean and Hilbertian settings of discrete and continuous probability distributions. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to compare the proof of the existence and uniqueness of fixed points for T -contractive mappings in various metric spaces and different distances regarding some techniques in mathematical analysis. Also, several comparisons to show the efficiency of the obtained result will be considered. [ABSTRACT FROM AUTHOR]

In this paper, some fixed-point theorems are stated and proved in S-multiplicative metric spaces. We also show in this paper that some fixed-point results for various S-multiplicative metric spaces are equivalent to those of corresponding fixed-point results in S-metric spaces. Some examples are presented to validate the originality and applicability of our main results. [ABSTRACT FROM AUTHOR]

A recent theorem by T. Barthel, M. Hausmann, N. Naumann, T. Nikolaus, J. Noel, and N. Stapleton says that if A is a finite abelian p-group of rank r, then any finite A-space X which is acyclic in the nth Morava K-theory with n ⩾ r will have its subspace XA of fixed points acyclic in the (n - r)th Morava Ktheory. This is a chromatic homotopy version of P. A. Smith's classical theorem that if X is acyclic in mod p homology, then so is XA. The main purpose of this paper is to give an elementary proof of this new theorem that uses minimal background, and follows, as much as possible, the reasoning in standard proofs of the classical theorem. We also give a new fixed point theorem for finite dimensional, but possibly infinite, A-CW complexes, which suggests some open problems. [ABSTRACT FROM AUTHOR]

The fundamental goal of our paper is to study θ-convex contractive mappings in metric spaces. We demonstrate some fixed point results for such mappings. Also, we give an application to integral equations of our results. Consequently, our results encompass numerous generalizations of the Banach contraction principle on metric space. [ABSTRACT FROM AUTHOR]

This paper studies Markov stopping games with two players on a denumerable state space. At each decision time player II has two actions: to stop the game paying a terminal reward to player I, or to let the system to continue it evolution. In this latter case, player I selects an action affecting the transitions and charges a running reward to player II. The performance of each pair of strategies is measured by the risk-sensitive total expected reward of player I. Under mild continuity and compactness conditions on the components of the model, it is proved that the value of the game satisfies an equilibrium equation, and the existence of a Nash equilibrium is established. [ABSTRACT FROM AUTHOR]

This work studies a mathematical model involving a dynamic contact between two elasto-viscoplastic piezoelectric bodies with damage. The contact is modeled on a combination of a normal compliance and a normal damped response law associated with friction. We derive a variational formulation of the problem and we prove the existence and uniqueness result of the weak solution. The proof is based on the classical existence and uniqueness result for parabolic inequalities, differential equations and fixed-point arguments. This paper examines a friction problem between two piezoelectric bodies that are elastic- viscoplastic. The study uses both numerical and analytical methods. The contact surface is assumed to have a thin layer of lubricant, and a damped response contact condition is considered. The problem also takes into account electrical and frictional effects. The paper proves the existence of a unique weak solution to the problem by using variational inequalities and a fixed point argument. Additionally, a fully discrete approximation is investigated using the Euler scheme and finite element method for the spatial variable and time derivatives. Error estimates are then calculated, leading to convergence results under certain regularity conditions. [ABSTRACT FROM AUTHOR]

The present paper is on fixed point theory in set valued analysis. Here putting several concepts together, we define a set valued contraction and establish that such contractions have fixed points in a complete metric space. We have two main theorems in one of which we use α -regularity condition of the space as a substitute of the continuity requirement on the multivalued contraction. There are some illustrative examples and corollaries. We also perform stability analysis of fixed point sets. We establish that the fixed point sets associated with the mappings we consider in our theorems are stable. In the last section we discuss some consequences of the main results of this paper. [ABSTRACT FROM AUTHOR]

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]

In this paper, a (p , q) -fractional nonlinear difference equation of different orders is considered and discussed. With the help of (p , q) -calculus for integrals and derivatives properties, we convert the main integral boundary value problem (IBVP) to an equivalent solution in the form of an integral equation, we use the upper–lower solution technique to prove the existence of positive solutions. We present an example of the IBVP to apply and demonstrate the results of our method. [ABSTRACT FROM AUTHOR]

Recently, the fixed-point theorem for fuzzy contractive mappings has been investigated within the framework of intuitionistic fuzzy metric-like spaces. This interesting topic was explored through the utilization of G-Cauchy sequences as defined by Grabiec. The aim of this study is to enhance the aforementioned results in a few aspects. Initially, the proof of the fixed-point theorem is simplified and condensed, allowing for potential generalization to papers focusing on similar fixed-point analyses. Furthermore, instead of G-Cauchy sequences, the classical Cauchy sequences proposed by George and Veeramani are examined, incorporating an additional condition on the fuzzy metric. Within this context, a solution to an old unresolved question posed by Gregory and Sapena is provided. The findings are reinforced by relevant examples. Finally, the introduced fuzzy metrics are applied to the field of image processing. [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]

In this paper, we investigate the dynamics of Boolean networks by using their matrices of support. We derive properties about the transients, fixed points, and limit cycles. We also study the graph properties of the phase spaces of Boolean networks, and show how to use matrices of support to construct Boolean networks with prescribed dynamics. [ABSTRACT FROM AUTHOR]

Since the 1970s and 1980s, significant contributions have been made by Weiss, Butnariu, Heilpern, Chitra, Subrahmanyam, and others, extending fixed-point theorems to fuzzy mappings and topological spaces. This paper provides two generalizations of two important fixed-point theorems, one provided by Butnariu and the other provided by Chitra. The first generalization ensures that, under certain conditions, an acyclic fuzzy mapping has a fixed point. The second result ensures the existence of a point in the intersection of two or more fuzzy mappings considering contractible finite dimensional ANR spaces, which is a generalization of the statement provided by Chitra. [ABSTRACT FROM AUTHOR]

Let C denote a convex subset within the vector space p (·) , and let T represent a mapping from C onto itself. Assume α = (α 1 , ⋯ , α n) is a multi-index in [ 0 , 1 ] n such that ∑ i = 1 n α i = 1 , where α 1 > 0 and α n > 0 . We define T α : C → C as T α = ∑ i = 1 n α i T i , known as the mean average of the mapping T. While every fixed point of T remains fixed for T α , the reverse is not always true. This paper examines necessary and sufficient conditions for the existence of fixed points for T, relating them to the existence of fixed points for T α and the behavior of T-orbits of points in T's domain. The primary approach involves a detailed analysis of recurrent sequences in R. Our focus then shifts to variable exponent modular vector spaces p (·) , where we explore the essential conditions that guarantee the existence of fixed points for these mappings. This investigation marks the first instance of such results in this framework. [ABSTRACT FROM AUTHOR]

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]

In this paper, we deal with the strong convergence of the iteration scheme given by Akutsah et al., for mean nonexpansive mappings in uniformly convex Banach space endowed with directed graph. Also, we show fastness of Akutsah et al. iteration scheme with some well-known iteration schemes with the help of numerical examples. We, also present an application of fixed point theory in solution of integral equation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the use of Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a new two-dimensional γ -Ricker population model. Through the use of such transcendental functions, it is possible to study the fixed points and the respective eigenvalues of this exponential diffeomorphism as analytical expressions. Consequently, the maximum number of fixed points is proved, depending on whether the Allee effect parameter γ is even or odd. In addition, the analysis of the bifurcation structure of this γ -Ricker diffeomorphism, also taking into account the parity of the Allee effect parameter, demonstrates the results established using the Lambert W functions. Numerical studies are included to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we provide some appropriate conditions for the existence of solutions for a perturbed fractional neutral integro-differential system under the deformable derivative in a Banach space. Using the Banach contraction principle and Krasnoselskii's fixed point theorem, we establish some new existence theorems. Moreover, we provide two numerical examples to demonstrate the applicability of the theoretical results [ABSTRACT FROM AUTHOR]

This paper discusses the existence of solutions to fourth order nonlinear boundary value problem involving systems of differential equations and two point boundary conditions. The nonlinearity f ∈ C([0, 1] × R+n × Rn × Rn × Rn, Rn) considered in this paper includes derivatives up to order three. Using recent fixed point results for the sum of two operators, we impose a growth condition on f to establish new existence criterion that ensure the existence of at least one and the existence of at least two nonnegative solutions. [ABSTRACT FROM AUTHOR]

Copyright of Iraqi Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) 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.)

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]

The paper examines fixed point outcomes for the two-variable operator F acting in Fréchet algebras. These results can be viewed as modifications of the fixed point theorem for the C + A B operator within a wider context. Through our primary findings, we can establish the existence of solutions for nonlinear integral equations with deviations that are not bounded. The proofing technique employed also allows for an added description of the asymptotic stability of the solutions of the relevant equation. [ABSTRACT FROM AUTHOR]

This paper deals with some existence of solutions for some classes of coupled systems of conformable fractional differential equations with initial and boundary conditions in Banach and Fréchet spaces. Our results are based on some fixed point theorems. Some illustrative examples are presented in the last section. [ABSTRACT FROM AUTHOR]