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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]

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]

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]

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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]

This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss some results concerning the demiclosedness principle of generalized, nonexpansive mappings in uniformly convex spaces. Further, we present some new fixed-point theorems for generalized nonexpansive mappings in different settings of Banach spaces. [ABSTRACT FROM AUTHOR]

The current paper introduces a novel generalization of cone metric spaces called type I and type II composed cone metric spaces. Therefore, examples of a type I and type II composed cone metric space, which is not a cone metric space, are given. We establish some results of fixed point precisely about Hardy–Rogers type contraction on C2CMS and provide examples. Finally, we present an application of our results and how our results solve the Fredholm integral equation of generalizing several existing and unique fixed point theorems. [ABSTRACT FROM AUTHOR]

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. However, due to the complexity involved in the nature of fuzzy metrics, the authors need to develop innovative machinery to establish new fixed point theorems in such kind of spaces. In this paper, we propose the concepts of asymptotic fuzzy ψ-contractive and asymptotic fuzzy Meir-Keeler mappings, and describe some new machinery by which the corresponding fixed point theorems are proved. In this sense, the techniques used for the proofs in Section 5 are completely new. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the definition of a convex extended s-metric space and establish the existence of fixed points for some contraction mappings in convex extended s-metric spaces. Additionally, we provide several examples to validate our findings. Furthermore, we apply the main results to approximate solutions of the Fredholm integral equation. [ABSTRACT FROM AUTHOR]

In order to approximate the common solution of quasi-nonexpansive fixed point and pseudo-monotone variational inequality problems in real Hilbert spaces, this paper presented three new modified sub-gradient extragradient-type methods. Our algorithms incorporated viscosity terms and double inertial extrapolations to ensure strong convergence and to speed up convergence. No line search methods of the Armijo type were required by our algorithms. Instead, they employed a novel self-adaptive step size technique that produced a non-monotonic sequence of step sizes while also correctly incorporating a number of well-known step sizes. The step size was designed to lessen the algorithms' reliance on the initial step size. Numerical tests were performed, and the results showed that our step size is more effective and that it guarantees that our methods require less execution time. We stated and proved the strong convergence of our algorithms under mild conditions imposed on the control parameters. To show the computational advantage of the suggested methods over some wellknown methods in the literature, several numerical experiments were provided. To test the applicability and efficiencies of our methods in solving real-world problems, we utilized the proposed methods to solve optimal control and image restoration problems. [ABSTRACT FROM AUTHOR]

In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition Bγ,μ. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory. [ABSTRACT FROM AUTHOR]

This paper presents the stability theorem for the T-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning T-mean nonexpansive mappings within b-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically. [ABSTRACT FROM AUTHOR]

The aim of this paper was to provide systematic approaches to study the existence of results for the system fractional relaxation integro-differential equations. Applied problems require definitions of fractional derivatives, allowing the utilization of physically interpretable boundary conditions. Impulsive conditions serve as basic conditions to study the dynamic processes that are subject to sudden changes in their state. In the process, we converted the given fractional differential equations into an equivalent integral equation. We constructed appropriate mappings and employed the Schaefer's fixed-point theorem and the Banach fixed-point theorem to show the existence of a unique solution. We presented an example to show the applicability of our results. [ABSTRACT FROM AUTHOR]

This paper combines the concept of an arbitrary binary connection with the widely recognized principle of θ -contraction to investigate the innovative features of vector-valued metric spaces. This methodology demonstrates the existence of fixed points for both single- and multi-valued mappings within complete vector-valued metric spaces. Through the utilization of binary relations and θ -contraction, this study advances and refines the Perov-type fixed-point results in the literature. Furthermore, this article furnishes examples to substantiate the validity of the presented results. Additionally, we establish an application for finding the existence of solutions to a system of matrix equations. [ABSTRACT FROM AUTHOR]