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Fixed-point theory, which has been developing since 1922, is widely used. Various contraction principles have been defined in the literature. In this work, we define rational-type contraction and weak Choudhury type contraction using α -series in F-metric spaces and prove common fixed-point theorems for sequences of self-mappings. This method is based on the convergence series of coefficients. Our results are the generalized version of the results in the literature. Finally, we apply our main results to solve an integral equation and a differential equation. [ABSTRACT FROM AUTHOR]

This paper is devoted to showing the relevance of the notion of completeness used to establish a fixed point theorem in fuzzy metric spaces introduced by Kramosil and Michalek. Specifically, we show that demanding a stronger notion of completeness, called p-completeness, it is possible to relax some extra conditions on the space to obtain a fixed point theorem in this framework. To this end, we focus on a fixed point result, proved by Mihet for complete non-Archimedean fuzzy metric spaces (Theorem 1). So, we define a weaker concept than the non-Archimedean fuzzy metric, called t-strong, and we establish an alternative version of Miheţ's theorem for p-complete t-strong fuzzy metrics (Theorem 2). In addition, an example of t-strong fuzzy metric spaces that are not non-Archimedean is provided. [ABSTRACT FROM AUTHOR]

The primary objective of the paper is to present the Banach contraction theorem in soft fuzzy metric spaces while taking into consideration a restriction on the soft fuzzy metric between the soft points of the absolute soft set. A new altering distance function, namely the Ψ -contraction function, is introduced on soft fuzzy metric spaces, and some fixed point results are proven by considering soft mappings that comprise Ψ -contraction with the continuity of soft t-norm. In addition to that, some illustrations are supplied for the support of the established soft fuzzy Banach contraction theorem and fixed point results over Ψ -contraction mappings. The obtained results generalize and extend some well-known results present in the literature on fixed point theory. [ABSTRACT FROM AUTHOR]

Gregori and Romaguera introduced, in 2004, the notion of a KM-fuzzy quasi-metric space as a natural asymmetric generalization of the concept of fuzzy metric space in the sense of Kramosil and Michalek. Ever since, various authors have discussed several aspects of such spaces, including their topological and (quasi-)metric properties as well as their connections with domain theory and their relationship with other fuzzy structures. In particular, the development of the fixed point theory for these spaces and other related ones, such as fuzzy partial metric spaces, has received remarkable attention in the last 15 years. Continuing this line of research, we here establish general fixed point theorems for left and right complete Hausdorff KM-fuzzy quasi-metric spaces, which are applied to deduce characterizations of these distinguished kinds of fuzzy quasi-metric completeness. Our approach, which mixes conditions of Suzuki-type with contractions of α − ϕ -type in the well-known proposal of Samet et al., allows us to extend and improve some recent theorems on complete fuzzy metric spaces. The obtained results are accompanied by illustrative and clarifying examples. [ABSTRACT FROM AUTHOR]

Partial metrics constitute a generalization of classical metrics for which self-distance may not be zero. They were introduced by S.G. Matthews in 1994 in order to provide an adequate mathematical framework for the denotational semantics of programming languages. Since then, different works were devoted to obtaining counterparts of metric fixed-point results in the more general context of partial metrics. Nevertheless, in the literature was shown that many of these generalizations are actually obtained as a corollary of their aforementioned classical counterparts. Recently, two fuzzy versions of partial metrics have been introduced in the literature. Such notions may constitute a future framework to extend already established fuzzy metric fixed point results to the partial metric context. The goal of this paper is to retrieve the conclusion drawn in the aforementioned paper by Haghia et al. to the fuzzy partial metric context. To achieve this goal, we construct a fuzzy metric from a fuzzy partial metric. The topology, Cauchy sequences, and completeness associated with this fuzzy metric are studied, and their relationships with the same notions associated to the fuzzy partial metric are provided. Moreover, this fuzzy metric helps us to show that many fixed point results stated in fuzzy metric spaces can be extended directly to the fuzzy partial metric framework. An outstanding difference between our approach and the classical technique introduced by Haghia et al. is shown. [ABSTRACT FROM AUTHOR]

Modular metric space is one of the most interesting spaces in the framework of the metric fixed point theory. The main goal of the paper is to provide some certain fixed point results in the context of modular metric spaces and non-Archimedean modular metric spaces. In particular, we examine the existence of interpolative Meir–Keeler contraction types via admissible mappings for fixed point theory. Our results bring together several results available in the current corresponding literature. [ABSTRACT FROM AUTHOR]

Inspired by the ideas of R. Kannan, we define the new concepts of mutual Kannan contractivity and mutual contractivity between two self-maps on a metric space that generalize the concepts of the Kannan map and contraction. We give some examples and deduce the properties of the operators satisfying this type of condition; in particular, we study the case where the space is normed, and the maps are linear. Then we generalize some theorems proposed by this author on the existence of a fixed point of one operator or a common fixed point for two operators. Our results first prove the existence of a common fixed point of a set of self-maps of any cardinal number (countable or uncountable) satisfying the conditions of Kannan type in metric spaces. The same is proved for a set of maps satisfying the mutual relations of classical contractivity. We prove in both cases the convergence of iterative schemes involving operators with mutual relations of contractivity, proposing sufficient conditions for the iteration of the operators on any element of the space to converge to the common fixed point when a different operator is taken in each step. The results obtained are applied to operators acting on real functions, coming from the fractal convolution with the null function. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a new concept of Z-Z-B spaces, which is a generalization of Z-C-X spaces. Meanwhile, the new concept of the superior cone is introduced. Secondly, we study some new problems for semi-closed 1-set-contractive operators in the Z-Z-B space and obtain some new results. These new theorems are proven by combining partial order theory with fixed point index theory. Regarding these theorems, in the latter part of the paper, the proofs are omitted since the methods of proving these theorems are similar. Moreover, two important inequality lemmas are proven. [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]

In this paper, we investigate the existence and uniqueness of a fixed point of almost contractions via simulation functions in metric spaces. Moreover, some examples and an application to integral equations are given to support availability of the obtained results. [ABSTRACT FROM AUTHOR]

We prove the generalized Hyers–Ulam stability of a mean value type functional equation f (x) - g(y) = (x - y)h(x + y) by applying a method originated from fixed point theory. [ABSTRACT FROM AUTHOR]

In the present article, we introduce the new concept of start point in a directed graph and provide the characterizations required for a directed graph to have a start point. We also define the notion of a self path set valued map and establish its relation with start point in the setting of a metric space endowed with a directed graph. Further, some fixed point theorems for set valued maps have been proven in this context. A version of the Knaster-Tarski theorem has also been established using our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new notion of Suzuki-type (a, b, q, g)-contractive mapping and investigate the existence and uniqueness of the best proximity point for such mappings in non-Archimedean modular metric space using the weak Pl-property. Meanwhile, we present an illustrative example to emphasize the realized improvements. These obtained results extend and improve certain well-known results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, inspired by the concept of b-metric space, we introduce the concept of extended b-metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our results extend/generalize many pre-existing results in literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain some common fixed point theorems for generalized contractions involving certain control functions in controlled metric space and derive some generalized fixed point results as a consequence of our main results. We also prove some common fixed point theorems in controlled metric spaces endowed with a graph. Our results will generalize and amend many famous results from the literature. We also provide an example to show the authenticity of the established results. As an application of our main result, we investigate the solution of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we prove a Sehgal–Guseman-type fixed point theorem in b-rectangular metric spaces which provides a complete solution to an open problem raised by Zoran D. Mitrović (A note on a Banach's fixed point theorem in b-rectangular metric space and b-metric space). The result presented in the paper generalizes and unifies some results in fixed point theory. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to introduce and study some fixed point results for rational multivalued G-contraction and F-Khan-type multivalued contraction mappings on a metric space with a graph. At the end, we give an illustrative example. [ABSTRACT FROM AUTHOR]

The present paper aims to introduce the concept of weak-fuzzy contraction mappings in the graph structure within the context of fuzzy cone metric spaces. We prove some fixed point results endowed with a graph using weak-fuzzy contractions. By relaxing the continuity condition of mappings involved, our results enrich and generalize some well-known results in fixed point theory. With the help of new lemmas, our proofs are straight forward. We furnish the validity of our findings with appropriate examples. This approach is completely new and will be beneficial for the future aspects of the related study. We provide an application of integral equations to illustrate the usability of our theory. [ABSTRACT FROM AUTHOR]

One of the main goals of this paper is to obtain new contractive conditions using the method of a strictly increasing mapping F : (0 , + ∞) → (− ∞ , + ∞) . According to the recently obtained results, this was possible (Wardowski's method) only if two more properties (F 2) and (F 3) were used instead of the aforementioned strictly increasing (F 1) . Using only the fact that the function F is strictly increasing, we came to new families of contractive conditions that have not been found in the existing literature so far. Assuming that α (u , v) = 1 for every u and v from metric space Ξ , we obtain some contractive conditions that can be found in the research of Rhoades (Trans. Amer. Math. Soc. 1977, 222) and Collaco and Silva (Nonlinear Anal. TMA 1997). Results of the paper significantly improve, complement, unify, generalize and enrich several results known in the current literature. In addition, we give examples with results in line with the ones we obtained. [ABSTRACT FROM AUTHOR]

We propose a notion of w-distance for fuzzy metric spaces, in the sense of Kramosil and Michalek, which allows us to obtain a characterization of complete fuzzy metric spaces via a suitable fixed point theorem that is proved here. Our main result provides a fuzzy counterpart of a renowned characterization of complete metric spaces due to Suzuki and Takahashi. [ABSTRACT FROM AUTHOR]

In this study, we introduce set-valued Prešić type almost contractive mapping, Prešić type almost F-contractive mapping and set-valued Prešić type almost F-contractive mapping in metric space and prove some fixed point results for these mappings. Additionally, we give examples to show that our main theorems are applicable. These examples show that the new class of set-valued Prešić type almost F-contractive operators is not included in Prešić type class of set-valued Prešić type almost contractive operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of d * -complete topological spaces, which include earlier defined classes of complete metric spaces and quasi b-metric spaces. Further, we prove some fixed point results for mappings defined on d * -complete topological spaces, generalizing earlier results of Tasković, Ćirić and Prešić, Prešić, Bryant, Marjanović, Yen, Caccioppoli, Reich and Bianchini. [ABSTRACT FROM AUTHOR]

In this paper we consider a kind of Geraghty contractions by using m w -distances in the setting of complete quasi-metric spaces. We provide fixed point theorems for this type of mappings and illustrate with some examples the results obtained. [ABSTRACT FROM AUTHOR]

In the present work, we study many fixed point results in intuitionistic generalized fuzzy cone metric space. Precisely, we prove new common fixed point theorems for three self mappings that do not require any commutativity or continuity but a generalized contractive condition. Our results are generalizations for many results in the literature. Some examples are given to support these results. [ABSTRACT FROM AUTHOR]

In this paper, we enlarge the class of C * -algebra valued partial metric spaces as well as the class of C * -algebra valued b-metric spaces by introducing the class of C * -algebra valued partial b-metric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result in order to examine the existence and uniqueness of a solution for the system of Fredholm integral equations. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to introduce the ( α , β )-type ϑ -contraction, ( α , β )-type rational ϑ -contraction, and cyclic ( α - ϑ ) contraction. Based on these definitions we prove fixed point theorems in the complete metric spaces. These results extend and improve some known results in the literature. As an application of the proved fixed point Theorems, we study the existence of solutions of an integral boundary value problem for scalar nonlinear Caputo fractional differential equations with a fractional order in (1,2). [ABSTRACT FROM AUTHOR]

We present a condition that guarantees the existence and uniqueness of fixed (or best proximity) points in complete metric space (or uniformly convex Banach spaces) for a wide class of cyclic maps, called p–cyclic summing maps. These results generalize some known results from fixed point theory. We find a priori and a posteriori error estimates of the fixed (or best proximity) point for the Picard iteration associated with the investigated class of maps, provided that the modulus of convexity of the underlying space is of power type. We illustrate the results with some applications and examples. [ABSTRACT FROM AUTHOR]

In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0 ) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b-metric spaces because they allow to consider some families of functions endowed with b-metrics deriving from similarity measures that are more general than norms. Taking into account that the contractivity condition we will employ is very general (of Hardy-Rogers type), we will discuss the validation and usage of this novel condition. After that, we introduce the main results of this paper and, finally, we deduce some consequences of them which illustrates the wide applicability of the main results. [ABSTRACT FROM AUTHOR]

The concepts of b-metric spaces and ω t -distance mappings play a key role in solving various kinds of equations through fixed point theory in mathematics and other science. In this article, we study some fixed point results through these concepts. We introduce a new kind of function namely, H -simulation function which is used in this manuscript together with the notion of ω t -distance mappings to furnish for new contractions. Many fixed point results are proved based on these new contractions as well as some examples are introduced. Moreover, we introduce an application on matrix equations to focus on the importance of our work. [ABSTRACT FROM AUTHOR]

In this manuscript we discuss, consider, generalize, improve and unify several recent results for so-called F-contraction-type mappings in the framework of complete metric spaces. We also introduce (φ , F) -weak contraction and establish the corresponding fixed point result. Using our new approach for the proof that a Picard sequence is a Cauchy in metric space, our obtained results complement and enrich several methods in the existing literature. At the end we give one open question for F-contraction of Ćirić-type mapping. [ABSTRACT FROM AUTHOR]

The aim of this article is to introduce a new class of contraction-like mappings, called the almost multivalued ( Θ , δ b )-contraction mappings in the setting of b-metric spaces to obtain some generalized fixed point theorems. As an application of our main result, we present the sufficient conditions for the existence of solutions of Fredholm integral inclusions. An example is also provided to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some common fixed point theorems for two distinct self-mappings in the setting of metric spaces by using the notion of a simulation function introduced in 2015. The contractivity conditions have not to be verified for all pairs of points of the space because it is endowed with an antecedent conditions. They are also of rational type because the involved terms in the contractivity upper bound are expressed, in some cases, as quotients. [ABSTRACT FROM AUTHOR]

In this article, we introduce a relatively new concept of multi-valued (θ , R) -contractions and utilize the same to prove some fixed point results for a special class of multi-valued mappings in metric spaces endowed with an amorphous binary relation. Illustrative examples are also provided to exhibit the utility of our results proved herein. Finally, we utilize some of our results to investigate the existence and uniqueness of a positive solution for the integral equation of Volterra type. [ABSTRACT FROM AUTHOR]

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces lp(·). We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define generalized ( α β - ψ) -contraction in the context of F -metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay ϑ / (ι) = − ρ 1 (ι) ϑ (ι) + ρ 2 (ι) L (ϑ (ι − ς (ι))) + ρ 3 (ι) ϑ / (ι − ς (ι)) , where ρ 1 (ι) , ρ 2 (ι) are continuous, ρ 3 (ι) is continuously differentiable and ς (ι) > 0 , for all ι ∈ R and is twice continuously differentiable. [ABSTRACT FROM AUTHOR]

The main aim of the current paper is the investigation of possibilities for improvements and generalizations contractive condition of Ćirić in the fuzzy metric spaces. Various versions of fuzzy contractive conditions are studied in two directions. First, motivated by recent results, more general contractive conditions in fuzzy metric spaces are achieved and secondly, quasi-contractive type of mappings are investigated in order to obtain fixed point results with a wider class of t-norms. [ABSTRACT FROM AUTHOR]

With the help of C-contractions having a fixed point, we obtain a characterization of complete fuzzy metric spaces, in the sense of Kramosil and Michalek, that extends the classical theorem of H. Hu (see "Am. Math. Month. 1967, 74, 436–437") that a metric space is complete if and only if any Banach contraction on any of its closed subsets has a fixed point. We apply our main result to deduce that a well-known fixed point theorem due to D. Mihet (see "Fixed Point Theory 2005, 6, 71–78") also allows us to characterize the fuzzy metric completeness. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of Caputo fractional q-difference inclusions in Banach spaces. We obtain some existence results by using the set-valued analysis, the measure of noncompactness, and the fixed point theory (Darbo and Mönch's fixed point theorems). Finally we give an illustrative example in the last section. We initiate the study of fractional q-difference inclusions on infinite dimensional Banach spaces. [ABSTRACT FROM AUTHOR]

Kannan maps have inspired a branch of metric fixed point theory devoted to the extension of the classical Banach contraction principle. The study of these maps in modular vector spaces was attempted timidly and was not successful. In this work, we look at this problem in the variable exponent sequence spaces ℓ p (·) . We prove the modular version of most of the known facts about these maps in metric and Banach spaces. In particular, our results for Kannan nonexpansive maps in the modular sense were never attempted before. [ABSTRACT FROM AUTHOR]

In a recent work, we established the existence of a unique fixed point for nonlinear contractive self-mappings of a bounded and closed set in a Banach space. In the present paper we extend this result to the case of unbounded sets. [ABSTRACT FROM AUTHOR]

We obtain a characterization of Hausdorff left K-complete quasi-metric spaces by means of α – ψ -contractive mappings, from which we deduce the somewhat surprising fact that one the main fixed point theorems of Samet, Vetro, and Vetro (see "Fixed point theorems for α – ψ -contractive type mappings", Nonlinear Anal.2012, 75, 2154–2165), characterizes the metric completeness. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present some topological properties in E-metric spaces such as the properties of e-sequences, the decision conditions of e-Cauchy sequences, the characteristics of non-normal cones, and so on. Moreover, the theorem of nested closed-balls in such spaces is displayed. In addition, some principal applications to fixed point theory are also given. [ABSTRACT FROM AUTHOR]

In this paper, we consider the recently introduced C A T p (0) , where the comparison triangles belong to ℓ p , for p ≥ 2 . We first establish an inequality in these nonlinear metric spaces. Then, we use it to prove the existence of fixed points of asymptotically nonexpansive mappings defined in C A T p (0) . Moreover, we discuss the behavior of the successive iteration introduced by Schu for these mappings in Banach spaces. In particular, we prove that the successive iteration generates an approximate fixed point sequence. [ABSTRACT FROM AUTHOR]

The aim of this study is to investigate the existence of solutions for the following Fredholm integral inclusion φ (t) ∈ f (t) + ∫ 0 1 K (t , s , φ (s)) ϱ s for t ∈ [ 0 , 1 ] , where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v (R) a given multivalued operator, where K c v represents the family of non-empty compact and convex subsets of R , φ ∈ C [ 0 , 1 ] is the unknown function and ϱ is a metric defined on C [ 0 , 1 ] . To attain this target, we take advantage of fixed point theorems for α -fuzzy mappings satisfying a new class of contractive conditions in the context of complete metric spaces. We derive new fixed point results which extend and improve the well-known results of Banach, Kannan, Chatterjea, Reich, Hardy-Rogers, Berinde and Ćirić by means of this new class of contractions. We also give a significantly non-trivial example to support our new results. [ABSTRACT FROM AUTHOR]

In this manuscript, we propose a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces. Besides this main goal, we also aim to combine and merge several existing fixed point theorems that were formulated by linear and nonlinear contractions. [ABSTRACT FROM AUTHOR]

The aim of this work is to extend the Mizoguchi-Takahashi fixed point result motivated by the approach of Wardowski (2012) and provide some related fixed point results in (ordered) metric spaces. An example is given to support the main results. Moreover, we provide an application on nonlinear differential equations. [ABSTRACT FROM AUTHOR]

In this manuscript, we introduce a new type of contraction, bilateral contraction which merges two significant approaches in the fixed point theory: Caristi type contractions and Jaggi type contractions. The principal aim of the main result is to enrich the literature by combining the techniques of the mentioned two celebrated results that belong to Jaggi and Caristi. We consider an example to indicate the validity and genuine nature of the main result. [ABSTRACT FROM AUTHOR]

In this paper, we present the concept of Θ − (σ , ξ) Ω -contraction mappings and we nominate some related fixed point results in ordered p-metric spaces. Our results extend several famous ones in the literature. Some examples and an application are given in order to validate our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the (𝒞 , Ψ * , G) class of contraction mappings using C-class functions and some improved control functions for a pair of set valued mappings as well as a pair of single-valued mappings, and prove common fixed point theorems for such mappings in a metric space endowed with a graph. Our results unify and generalize many important fixed point results existing in literature. As an application of our main result, we have derived fixed point theorems for a pair of α -admissible set valued mappings in a metric space. [ABSTRACT FROM AUTHOR]

In this manuscript, we introduce a new notion: a Berinde type (α , ψ) -contraction mapping. Thereafter, we investigate not only the existence, but also the uniqueness of a fixed point of such mappings in the setting of right-complete quasi-metric spaces. The result, presented here, not only generalizes a number of existing results, but also unifies several ones on the topic in the literature. An application of nonlinear fractional differential equations is given. [ABSTRACT FROM AUTHOR]