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Recently, fixed point results via E -contractions (also called P- contractions in some papers) for self-mappings in metric spaces have been investigated. Some results generalize the well - known Edelstein's theorem. In this paper, we provide some new fixed point theorems for mappings satisfying conditions of Edelstein - Suzuki type involving E -contractions. We also present several illustrative examples to compare our finding with some know results in the literature. [ABSTRACT FROM AUTHOR]

Ran and Reurings (Proc Am Math Soc 132(5):1435–1443, 2003) extended the Banach contraction principle to the setting of partially ordered metric spaces and recently Proinov (J Fixed Point Theory Appl 22:21, 2020) extended and unified many earlier fixed point theorems. In this paper we will present analogous results for the significantly wider class of mappings on preordered metric spaces. We give non-trivial examples of Kannan-type mappings. [ABSTRACT FROM AUTHOR]

We prove the existence and uniqueness of fixed points of some generalized contractible operators defined on modular G-metric spaces and also prove the modular G-continuity of such operators. Furthermore, we prove that some generalized weakly compatible contractive operators in modular G-metric spaces have a unique fixed point. Our results extend, generalize, complement and include several known results as special cases. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of the topological dimension of the set of solutions of the operator inclusion of the form , where A is a bounded linear surjective operator, and F is a multi-valued Lipschitz map with closed convex images. The resulting theorem establishes a connection between the dimension of the kernel of the operator A and the dimension of the set of solutions of this inclusion. [ABSTRACT FROM AUTHOR]

In this paper, we present some fixed point theorems for a class of contractive mappings in complete b-metric spaces of zero at infinity varieties. We verify the T-stability of Picard's iteration and the P property for such mapping. [ABSTRACT FROM AUTHOR]

We first study the asymptotic behavior of infinite products of nonexpansive selfmappings of a star-shaped complete metric space which is not necessarily bounded. Using the notion of contractivity and the Baire category approach, we show that a typical (generic) sequence of nonexpansive mappings is contractive and generates infinite products which have the same asymptotic behavior. This result is then applied to certain classes of nonexpansive set-valued self-mappings of a closed and star-shaped subset of a Banach space. It is shown that in these classes most (in the sense of Baire category) mappings are contractive. In particular, we show that this fact is true for a certain class of compact-valued mappings. It follows that a generic mapping in this class has a fixed point. [ABSTRACT FROM AUTHOR]

In the present paper a concept of $$C^*$$ -algebra-valued modular space is introduced which is a generalization of a modular space. Next, some fixed point theorems for self-maps with contractive or expansive conditions on such spaces are proved. [ABSTRACT FROM AUTHOR]

Meir and Keeler formulated their fixed point theorem for contractive mappings with purely metric condition. This idea was extended by numerous mathematicians. In this paper, we present a simple method of proving such theorems and give new results. [ABSTRACT FROM AUTHOR]

The aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi:]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler-Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of w-distances, and we prove existence theorems for single-valued mappings and set-valued mappings in a complete metric space which generalize Takahashi, Wong, and Yao's theorems. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of a fixed point of certain operators in the setting of complete quasi- b-metric-like spaces via admissible mappings. Our results improve, extend, and unify several well-known existence results. [ABSTRACT FROM AUTHOR]

Based on the concept and properties of $C^{\ast}$-algebras, the paper introduces a concept of $C^{\ast}$-algebra-valued b-metric spaces which generalizes the concept of $C^{\ast}$-algebra-valued metric spaces and gives some basic fixed point theorems for self-map with contractive condition on such spaces. As applications, existence and uniqueness results for a type of operator equation and an integral equation are given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two general iterative methods for a certain optimization problem of which the constrained set is the common set of the solution set of the variational inequality problem for a continuous monotone mapping and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Under some control conditions, we establish the strong convergence of the proposed methods to a common element of the solution set and the fixed point set, which is the unique solution of a certain optimization problem. As a direct consequence, we obtain the unique minimum-norm common point of the solution set and the fixed point set. [ABSTRACT FROM AUTHOR]

We survey recent results regarding genericity and porosity in fixed point theory. These results concern, inter alia, infinite products, nonexpansive mappings, approximate fixed points, contractive mappings, bounded linear regularity, set-valued mappings, holomorphic mappings and weak ergodic theorems. We consider both normed linear spaces and hyperbolic metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently. [ABSTRACT FROM AUTHOR]

In this manuscript we extend very recent fixed point theorems in the setting of Menger spaces in three senses: on the one hand, we introduce the notion of Menger probabilistic metric-like space by avoiding a non-necessary constraint (at least, for our purposes) in the properties that define a Menger space; on the other hand, we consider a more general class of auxiliary functions in the contractivity condition; finally, we show that the function $t\rightarrow1/t-1$ (which appears in many fixed point theorems in the fuzzy context) can be replaced by more appropriate and general functions. We illustrate our main statements with an example in which previous results cannot be applied. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point theorems on some extensions of Geragthy contractive type mappings in the context of b-metric-like spaces. [ABSTRACT FROM AUTHOR]

In this paper, we establish the structure of Menger PbM-spaces as a generalization of Menger PM-spaces. We present some fixed point theorems for a new class of contractive mappings in the framework of Menger PbM-spaces. We also provide examples to illustrate the results presented herein. Then we utilize our main result to obtain the existence and uniqueness of a solution for a Volterra type integral equation. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of fixed points for mappings defined on complete metric spaces, satisfying a general contractive inequality depending on two additional mappings. [ABSTRACT FROM AUTHOR]

Let S: A→ B and T: A→ B be given non-self mappings, where A and B are non-empty subsets of a metric space. As S and T are non-self mappings, the equations Sx= x and Tx= x do not necessarily have a common solution, called a common fixed point of the mappings S and T. Therefore, in such cases of non-existence of a common solution, it is attempted to find an element x that is closest to both Sx and Tx in some sense. Indeed, common best proximity point theorems explore the existence of such optimal solutions, known as common best proximity points, to the equations Sx= x and Tx= x when there is no common solution. It is remarked that the functions x→ d( x, Sx) and x→ d( x, Tx) gauge the error involved for an approximate solution of the equations Sx= x and Tx= x. In view of the fact that, for any element x in A, the distance between x and Sx, and the distance between x and Tx are at least the distance between the sets A and B, a common best proximity point theorem achieves global minimum of both functions x→ d( x, Sx) and x→ d( x, Tx) by stipulating a common approximate solution of the equations Sx= x and Tx= x to fulfill the condition that d( x, Sx)= d( x, Tx)= d( A, B). The purpose of this article is to elicit common best proximity point theorems for pairs of contractive non-self mappings and for pairs of contraction non-self mappings, yielding common optimal approximate solutions of certain fixed point equations. Besides establishing the existence of common best proximity points, iterative algorithms are also furnished to determine such optimal approximate solutions. [ABSTRACT FROM AUTHOR]

Let A and B be non-empty subsets of a metric space. As a non-self mapping $${T:A\longrightarrow B}$$ does not necessarily have a fixed point, it is of considerable interest to find an element x in A that is as close to Tx in B as possible. In other words, if the fixed point equation Tx = x has no exact solution, then it is contemplated to find an approximate solution x in A such that the error d( x, Tx) is minimum, where d is the distance function. Indeed, best proximity point theorems investigate the existence of such optimal approximate solutions, called best proximity points, to the fixed point equation Tx = x when there is no exact solution. As the distance between any element x in A and its image Tx in B is at least the distance between the sets A and B, a best proximity pair theorem achieves global minimum of d( x, Tx) by stipulating an approximate solution x of the fixed point equation Tx = x to satisfy the condition that d( x, Tx) = d( A, B). The purpose of this article is to establish best proximity point theorems for contractive non-self mappings, yielding global optimal approximate solutions of certain fixed point equations. Besides establishing the existence of best proximity points, iterative algorithms are also furnished to determine such optimal approximate solutions. [ABSTRACT FROM AUTHOR]

We establish two fixed point theorems for certain mappings of contractive type. The first result is concerned with the case where such mappings take a nonempty, closed subset of a complete metric space X into X, and the second with an application of the continuation method to the case where they satisfy the Leray–Schauder boundary condition in Banach spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to obtain an answer, in the setting of Menger PM-spaces, to the question on the existence of contractive mappings which admit discontinuity at the fixed point (see Rhoades in Contemp Math 72:233–245, 1988). [ABSTRACT FROM AUTHOR]