Search

In this work, we analyse the class of strictly pseudocontractive mappings in general metric spaces by providing a comprehensive and appropriate definition of a strictly pseudocontractive mapping, which serves as a natural extension of the existing notion. Moreover, we establish its various characterizations and explore several significant properties of these mappings in relation to fixed point theory in CAT(0) spaces. Specifically, we establish that these mappings are Lipschitz continuous, satisfying the demiclosedness-type property, and possessing a closed convex fixed point set. Furthermore, we show that the fixed points of the mappings can be effectively approximated using an iterative scheme for fixed points of nonexpansive mappings. The results in this work contribute to a deeper understanding of strictly pseudocontractive mappings and their applicability in the context of fixed point theory in metric spaces. [ABSTRACT FROM AUTHOR]

In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of classical metrics; therefore, for each value of the parameter, the positivity, the symmetry, the triangle inequality, or the continuity is ensured. Also, we demonstrate how analogous theorems in modular metric spaces may be used to generate the best proximity point results in triangular fuzzy metric spaces. The utility of our findings is further demonstrated by certain examples, illustrated consequences, and an application to fuzzy fractional differential equations. [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]

In the context of a complete metric space, the most important fixed-point result for multi-valued operators was given in 1969. Many extensions of this fixed-point principle for multi-valued operators were proved by different authors. Based on some of the above-mentioned results, we introduce the notion of the multi-valued Feng–Liu-type operator and we construct an abstract fixed-point theory for this general class of multi-valued operators. Our results extend and complement some theorems in metric fixed-point theory for multi-valued operators. An application to a Cauchy problem related to a first-order differential inclusion is also given. In this case, our theorem improves several previous theorems on this subject by relaxing the contraction-type condition (with respect to its second argument) on the multi-valued right-hand side. [ABSTRACT FROM AUTHOR]

Recently, Karapinar introduced a new Hardy-Rogers type contractive mapping using the concept of interpolation and proved a fixed point theorem in complete metric space. This new type of mapping, called "interpolative Hardy-Rogers type contractive mapping" is a generalization of Hardy-Rogers's fixed point theorem. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for cyclic mappings on complete metric spaces. Moreover, an example is given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

This article introduces the novel concept of an extended parametric S b -metric space, which is a generalization of both S b -metric spaces and parametric S b -metric spaces. Within this extended framework, we first establish an analog version of the Banach fixed-point theorem for self-maps. We then prove an improved version of the Banach contraction principle for symmetric extended parametric S b -metric spaces, using an auxiliary function to establish the desired result. Finally, we provide illustrative examples and an application for determining solutions to Fredholm integral equations, demonstrating the practical implications of our work. [ABSTRACT FROM AUTHOR]

In this paper, we use an inequality involving a coupled multivalued mapping and a singlevalued mapping to obtain a coupled coincidence point theorem. We discuss special conditions under which coupled common fixed point theorems are obtained. The result combines several ideas prevalent in fixed point theory studies. There are several corollaries and illustrative examples. The Hausdorff-Pompeiu metric between sets is used. The work is in the context of metric spaces and is a part of set-valued analysis with the singlevalued consequences. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a generalization of a fixed point theorem given by Popescu [O. Popescu, Comput. Math. Appl., vol. 62, no. 10, pp. 3912-3919, 2011]. An example is also given to support our main result. [ABSTRACT FROM AUTHOR]

In this paper, we prove a new coincidence and common fixed point theorem of hybrid mappings using the C-class function and T-weak commutativity. Finally, we give an example to illustrate our result. [ABSTRACT FROM AUTHOR]

Fixed point theory is a crucial branch in mathematics with a colossal number of applications in countless subjects. It furnishes preeminent tools and resources for elucidating varied problems which at first glance do not look like a fixed point problem. Since and even before 1912 till now several authors launched the existence and uniqueness of common fixed points for pairs of single and set-valued maps satisfying certain compatibilities on different spaces. This paper proves existence and uniqueness of a common fixed point for pairs of occasionally weakly biased maps. This unique common fixed point is guaranteed under the concept of modified contractive modulus function. Our theorems improve some results existing in the fixed point literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a common fixed point theory for a pair of multivalued operators in complete metric spaces. Existence and stability results for the common fixed point problem will be discussed. The approach is based on some fixed point results for multivalued graphical contractions and for multivalued operators of Feng-Liu type. Our results extend to the multivalued case some recent results in the literature. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce and prove some fixed point theorems for two maps that satisfy (φ—ψ)-contractive conditions with rational expression in partially ordered metric spaces, our results improve and unify a multitude of fixed point theorems and generalize some recent results in ordered partially metric space. [ABSTRACT FROM AUTHOR]

In the context of a complete metric space, we will consider the common fixed point problem for two self operators. The operators are assumed to satisfy a general contraction type condition inspired by the Ćirić fixed point theorems. Under some appropriate conditions we establish existence, uniqueness and approximation results for the common fixed point. In the same framework, the second problem is to study various stability properties. More precisely, we will obtain sufficient conditions assuring that the common fixed point problem is well-posed and has the Ulam–Hyers stability, as well as the Ostrowski property for the considered problem. Some examples and applications are finally given in order to illustrate the abstract theorems proposed in the first part of the paper. Our results extend and complement some theorems in the recent literature. [ABSTRACT FROM AUTHOR]

The purpose of this manuscript is to demonstrate the existence and uniqueness of triple fixed-point results for Geraghty-type contractions in ordinary metric spaces with binary relations. Moreover, the well-posedness of the tripled fixed point problem is investigated. Consequently, α -dominated mapping on such space is discussed. Ultimately, to promote our paper, some illustrative examples are derived, and the existence of the solution to a system of differential equations is obtained as an application. [ABSTRACT FROM AUTHOR]

In this paper, unique common fixed point theorems for pairs of subcompatible and reciprocally continuous mappings or compatible and subsequentially continuous mappings are obtained. This unique common fixed point is guaranteed under a new concept named a weak altering distance function. Our theorems improve some results especially the ones of [2]. [ABSTRACT FROM AUTHOR]

In this paper, some common fixed point theorems for pairs of subcompatible and reciprocally continuous mappings or compatible and subsequentially continuous mappings satisfying integral type are obtained. Our results improve several results especially the results of [3], Pathak et al. [13], Djoudi and Aliouche [6], Mbarki [10] and others. [ABSTRACT FROM AUTHOR]

We establish a coupled coincidence and common coupled fixed point theorem for hybrid pair of mappings under φ - ψ contraction on a noncomplete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. We also give an example to validate our result. We improve and generalize several known results. [ABSTRACT FROM AUTHOR]

A new contraction condition for multivalued maps in metric spaces is introduced and then, based on this new condition, we prove two fixed point theorems for such contractions. The new condition uses the altering distance technique and a Pompeiu type metric on the family of nonempty and closed subsets of a metric space. Our results essentially compliments and generalizes some well known results. As application, we model a nonconvex Hammerstein type integral inclusion and prove an existence theorem for this problem. [ABSTRACT FROM AUTHOR]

Introduction/purpose: This paper establishes some new results of Piri–Kumam–Dung-type mappings in a complete metric space.Тhe goal was to improve the already published results. Methods: Using the property of a strictly increasing function as well as the known Lemma formulated in (Radenović et al, 2017), the authors have proved that a Picard sequence is a Cauchy sequence. Results: New results were obtained concerning the F – contraction mappings of S in a complete metric space. To prove it, the authors used only property (W1). Conclusion: The authors believe that the obtained results represent a significant improvement of many known results in the existing literature. [ABSTRACT FROM AUTHOR]

In this manuscript, we introduce the notion of admissible hybrid Geraghty contraction and we investigate the existence of fixed points of such mappings in the setting of complete metric spaces. Our results not only extend and generalize several results in the fixed point theory literature, but also unify most of them. We give some corollaries to illustrate the novelty of the main result. [ABSTRACT FROM AUTHOR]

In this paper, we extend the results of Wardowski by applying some new conditions on the self map on a complete metric space, concerning the F-contractions defined by Wardowski. We present some fixed point results of Wardowski type. An example is given to demonstrate the novelty of our work. [ABSTRACT FROM AUTHOR]

In this chapter, neutrosophic triplet partial g - metric spaces are obtained. Then, some definitions and examples are given for neutrosophic triplet partial g - metric space. Based on these definitions, new theorems are given and proved. In addition, it is shown that neutrosophic triplet partial g - metric spaces are different from the classical g - metric spaces, neutrosophic triplet metric spaces. Thus, we add a new structure in neutrosophic triplet theory. Also, thanks to neutrosophic triplet partial g - metric space, researchers can obtain new fixed point theorems for neutrosophic triplet theory. [ABSTRACT FROM AUTHOR]

Triangular fuzzy normed space and demonstration of fixed-point theorems in normed space unescorted by any analytical structure is studied in this paper. Now we study space with a linear system but non-linear mapping is considered. We reduce our consideration to normed linear space our leading conclusions expanded to common locally convex space. [ABSTRACT FROM AUTHOR]

The aim of this paper is to initiate the study of best proximity point and optimal coincidence point results of some a Pata-proximal admissible contraction of type-I and type-II in the framework of complete metric space. Some examples are presented to support the results obtained herein. Our results unify, extend and generalize various existing results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we investigate one of the classical problems of the metric fixed point theory: Whether there is a contraction condition which does not force the mapping to be continuous at the fixed point. We propose a contraction conditions in rational form that has a unique fixed point but not necessarily continuous at the given fixed point. [ABSTRACT FROM AUTHOR]

In this paper, introduce the notion of an interpolative Hardy-Rogers type Z -contraction and we revisit the renowned Hardy-Rogers contraction in the framework of interpolation. We investigate the existence of fixed points for such mappings in the context of metric spaces and list the immediate consequences that cover some existing results in the literature. [ABSTRACT FROM AUTHOR]

In this work, we are interested to prove a general fixed point theorem for a mapping satisfying a new type of implicit relation in G-metric spaces. The results in this paper generalize the results obtained in [3], [7], [8], [10] and obtain other particular results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of extended parametric b-metric space and investigate the existence of fixed points for some contractive type mappings in such spaces. Consequently, we derive some new fixed point results in triangular ordered extended fuzzy b-metric spaces. Moreover, some examples and an application are provided here to illustrate the applicability of the obtained results. [ABSTRACT FROM AUTHOR]

A new Caristi-type inequality is considered and Caristi's fixed point theorem for mappings of complete metric spaces is developed (in both the single- and set-valued cases). On the basis of this development mappings of complete metric spaces which are contractions with respect to a function of two vector arguments are studied. This function is not required to be a metric or even a continuous function. The proved theorems are generalizations of the Banach contraction principle and Nadler's theorem. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of F − contraction via α − admissible pair of mappings. We also provide many common fixed point results regarding rational expressions in the setting of metric spaces. Moreover, we also present some illustrated examples as an application of this concept and we also establish an existence theorem for integral equations. [ABSTRACT FROM AUTHOR]

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that some of the published assertions based on these tools are incorrect or trivial; we offer improvements on others. [ABSTRACT FROM AUTHOR]

In this paper we generalize the notion of O-set and establish some fixed point theorems for ⊥ - α - ψ-contraction multifunction in the setting of orthogonal modular metric spaces. As consequences of these results we deduce some theorems in orthogonal modular metric spaces endowed with a graph and partial order. Finally, we establish some theorems for integral type contraction multifunctions and give some examples to demonstrate the validity of the results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new idea of α-C-class function and establish new fixed point results in a complete metric space. It can be stated that the results that have come into being give substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

The purpose of this article, we consider the existence of a unique best proximity point x* ∊ A such that d(x*, Tx*) = dist(A,B) for generalized φ-weak contraction mapping T : A → B, where A,B(6≠, θ) are subsets of a metric space (X, d): [ABSTRACT FROM AUTHOR]

In this article, we study coupled fixed point theorems in newly appeared JS-metric spaces. It is important to note that the class of JS-metric spaces includes standard metric spaces, dislocated metric spaces, b'-metric spaces, modular spaces etc. The purpose of this paper is to present several coupled fixed point results in a more general way. Moreover, the techniques used in our proofs are indeed different from the comparable existing literature. Finally, we present non-trivial examples to validate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we establish a common fixed point theorem for four self mappings satisfying an implicit relation, via weakly biased maps in metric space. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new idea of α-C-class function and establish new fixed point results in a complete metric space. It can be stated that the results that have come into being give substantial generalizations and improvements of several well known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

In this paper a general fixed point theorem for two pairs of mappings in two metric spaces, which generalize the results from [2] and [7], is proved. [ABSTRACT FROM AUTHOR]

In this paper, in complete metric spaces, we introduce random F-contraction and random F-weak contraction benefiting from the Wardowski and Van Dung's work. Later, we prove some random fixed point theorems in complete metric spaces. We also give some examples to support our results. [ABSTRACT FROM AUTHOR]

In this article, we consider Kannan-type contractive self-map T on a metric space (X, d) such that and establish some new fixed point results without taking the compactness of X and also relaxing the continuity of T. Further, we anticipate a result ensuring the completeness of the space X via fixed point property of this map. Finally, we give an affirmative answer to the open question posed by J. Górnicki [Fixed point theorems for Kannan-type mappings, J. Fixed Point Theory Appl. 2017]. Apart from these, our manuscript consists of several nontrivial examples which signify the motivation of our investigations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of α-ψ-contractive mapping of type E, to remedy of the weakness of the existing contraction mappings. We investigate the existence and uniqueness of a fixed point of such mappings. We also list some examples to illustrate our results that unify and generalize the several well-known results including the famous Banach contraction mapping principle. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain common fixed points of set mappings defined on a family of sets endowed with a graph satisfying Θ-contraction. Our results generalize and extend various results in the existing literature. We also provide some non trivial examples to support the validity of our main results. Some applications to the construction of common fixed points of set mappings in ε-chainable metric space are also discussed. [ABSTRACT FROM AUTHOR]

In this article, following the approach of F-contractions, we establish a common fixed point theorem for a pair of self-mappings satisfying F-contraction of rational type in complete metric spaces. An example is constructed to illustrate this result. An application to system of integral equations is presented. [ABSTRACT FROM AUTHOR]

New generalized forms of Banach and Kannan type contractions have been described and some coupled coincidence and coupled common fixed point results have been established in the setting of metric space involving a graph. Our theorems extend and generalize many existing results in the literature. Furthermore, an application to integral equations is presented to affirm the importance. [ABSTRACT FROM AUTHOR]

By various examples we illustrate that the ordered set theory is far away from having unitary notations and terminology. Some suggestions for unifiying the terminology are also presented. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show that the C-class function introduced by A. H. Ansari is a powerful weapon for the generalization of many important results in the theory of fixed points. [ABSTRACT FROM AUTHOR]

In this paper, a general coincidence and common fixed points theorem for two hybrid pairs of mappings satisfying property (E.A) is proved, generalizing the main results from [3] and [9]. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Geraghty result [7] to k-dimension. [ABSTRACT FROM AUTHOR]

Our work in this paper deals with some fixed point results for a class of nonexpansive single-valued and multi-valued mappings using Picard sequences in a complete metric space. Our results constitute generalizations of the corresponding results obtained by Demma et al. [6], Khojasteh et al. [11] and Vetro [15]. [ABSTRACT FROM AUTHOR]

In a recent paper [Pata, V., A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), No. 2, 299–305], the author stated and proved a fixed point theorem that is intended to generalize the well known Banach's contraction mapping principle. In this note we show that the main result in the above paper does not hold at least in two extremal cases for the parameter #949; involved in the contraction condition used there. We also present some illustrative examples and related results. [ABSTRACT FROM AUTHOR]