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Abstract In this paper, we introduce fuzzy generalized β-F-contractions as a generalization of fuzzy F-contractions with admissible mappings. We deduce sufficient conditions for the existence and uniqueness of fixed points for fuzzy generalized β-F-contractions in complete strong fuzzy metric spaces. Our results generalize several fixed-point results from the literature. We present an application of our main result.

In this paper, we introduce the b-triangular property in fuzzy b-metric space. Furthermore, we give some new fixed point results in fuzzy b-metric space for non-continuous mappings. Our results generalize and expand some results from the related literature. Two applications of our results, to solving Fredholm integral equation and in dynamic programming, are also given. [ABSTRACT FROM AUTHOR]

In this manuscript, we establish some fixed-point theorems without continuity by using the triangular property on a fuzzy bipolar b -metric space as a generalized version and expansion of the well-known results. We also provide some examples and applications of the integral equation to the solution for our main results. [ABSTRACT FROM AUTHOR]

In this manuscript, fixed point results without continuity via triangular notion on fuzzy bipolar metric spaces are established. The paper includes tangible examples which display the motivation for such investigations as those presented here. We solve an integral equation in this setting. The present work is a generalization of some published works.

These fundamental Theorems of classical analysis, namely Baire's Theorem and Cantor's Intersection Theorem in the context of Neutrosophic 2-metric spaces, are demonstrated in this article. Naschie discussed high energy physics in relation to the Baire's Theorem and the Cantor space in descriptive set theory. We describe, how to demonstrate the validity and uniqueness of the common fixed-point theorem for four mappings in Neutrosophic 2-metric spaces.

In this paper, contractive mappings of \CM{} type in fuzzy metric spaces are studied. A class $\Psi_1$ of gauge functions $\psi:(0,1]\to(0,1]$ such that, for any $r\in(0,1)$, there exists $\rho\in(r,1)$ such that $1-r> \tau >1-\rho$ implies $\psi(\tau)\geq 1-r$, is introduced, and it is shown that fuzzy $\psi$-contractive mappings are fuzzy contractive mappings of \CM{} type. A characterization of Cauchy sequences in fuzzy metric spaces is presented, and it is utilized to establish fixed point theorems. Examples are given to support the results. Our results cover those of Mihet (Fuzzy $\psi$-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets Syst. 159(2008) 739-744), Wardowski (Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 222(2013) 108-114) and others.

In this paper, orthogonal fuzzy versions are reported for some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J , S : (0 , 1 ] → (− ∞ , ∞) for the existence of fixed-points of (J , S) -fuzzy interpolative contractions. This way, many fixed point theorems are developed in orthogonal fuzzy metric spaces. We apply the (J , S) -fuzzy version of Banach fixed point theorem to demonstrate the existence and uniqueness of the solution. These results are supported with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations. [ABSTRACT FROM AUTHOR]

The symmetry of fuzzy metric spaces has benefits for flexibility, ambiguity tolerance, resilience, compatibility, and applicability. They provide a more comprehensive description of similarity and offer a solid framework for working with ambiguous and imprecise data. We give fuzzy versions of some celebrated iterative mappings. Further, we provide different concrete conditions on the real valued functions J , S : (0 , 1 ] → R for the existence of the best proximity point of generalized fuzzy (J , S) -iterative mappings in the setting of fuzzy metric space. Furthermore, we utilize fuzzy versions of J , S -proximal contraction, J , S -interpolative Reich–Rus–Ciric-type proximal contractions, J , S -Kannan type proximal contraction and J , S -interpolative Hardy Roger's type proximal contraction to examine the common best proximity points in fuzzy metric space. Also, we establish several non-trivial examples and an application to support our results. [ABSTRACT FROM AUTHOR]

This manuscript contains several fixed point results for α Γ -F-fuzzy contractive mappings in the framework of orthogonal fuzzy metric spaces. The symmetric property guarantees that the distance function is consistent and does not favour any one direction in orthogonal fuzzy metric spaces. No matter how the points are arranged, it enables a fair assessment of the separations between all of them. In fixed point results, the symmetry condition is preserved for several types of contractive self-mappings. Moreover, we provide several non-trivial examples to show the validity of our main results. Furthermore, we solve non-linear fractional differential equations, the Atangana–Baleanu fractional integral operator and Fredholm integral equations by utilizing our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce fuzzy generalized β-F-contractions as a generalization of fuzzy F-contractions with admissible mappings. We deduce sufficient conditions for the existence and uniqueness of fixed points for fuzzy generalized β-F-contractions in complete strong fuzzy metric spaces. Our results generalize several fixed-point results from the literature. We present an application of our main result. [ABSTRACT FROM AUTHOR]

In order to create a dynamic measure that describes distances between spatiotemporal points whose positions change over time as well as between the data represented by these points, a temporal intuitionistic fuzzy metric space is created in this paper. The notions of temporal fuzzy t-norm, temporal fuzzy tconorm, and temporal fuzzy negation which have not previously been discussed in the literature are defined, and some of their fundamental characteristics are investigated, in order to define this new method. The idea that the degrees of nearness and non-nearness change with time is the basis for a novel definition of the concept of temporal intuitionistic fuzzy metric spaces. However, the basic topological characteristics of the temporal intuitionistic fuzzy metric space are also looked at. We demonstrate how this new temporal metric space preserves the basic characteristics offered by both classical and fuzzy metric spaces. As a result, a new, more flexible, and dynamic metric topology is created while maintaining the fundamental topological characteristics of fuzzy and intuitionistic fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

In this manuscript, fixed point results without continuity via triangular notion on fuzzy bipolar metric spaces are established. The paper includes tangible examples which display the motivation for such investigations as those presented here. We solve an integral equation in this setting. The present work is a generalization of some published works. [ABSTRACT FROM AUTHOR]

In this study, we initiate the concept of fuzzy L - R -contraction and establish some fixed point results involving a G -transitive binary relation and fuzzy L -simulation functions, by employing suitable hypotheses on a fuzzy metric space endowed with a binary relation. The presented results unify, generalize, and improve various previous findings in the literature. [ABSTRACT FROM AUTHOR]

In the present paper, we prove common fixed point without continuity by using triangular property on fuzzy b-metric space. Our results generalize and expand some of the literature's well-known results. We also explore some of the application of our key results to Fredholm integral equation.

These fundamental Theorems of classical analysis, namely Baire's Theorem and Cantor's Intersection Theorem in the context of Neutrosophic 2-metric spaces, are demonstrated in this article. Naschie discussed high energy physics in relation to the Baire's Theorem and the Cantor space in descriptive set theory. We describe, how to demonstrate the validity and uniqueness of the common fixed-point theorem for four mappings in Neutrosophic 2-metric spaces. [ABSTRACT FROM AUTHOR]

Property A is a geometric property originally introduced for discrete metric spaces to provide a sufficient condition for coarse embeddability into Hilbert space, and it is defined via a Følner condition similar in spirit to the classical notion of amenability for groups. In this paper, we define property A for fuzzy metric spaces in the sense of George and Veeramani, show that it is an invariant in the coarse category of fuzzy metric spaces, and provide characterizations of it for uniformly locally finite fuzzy metric spaces. We also show that uniformly locally finite fuzzy metric spaces with property A are coarsely embeddable into Hilbert space. [ABSTRACT FROM AUTHOR]

Abstract We introduce the notion of generalized parametric metric spaces along with the study of its various properties. Further, we prove some new fixed point theorems for ( α , ψ ) $(\alpha ,\psi )$ -rational-type contractive mappings in generalized parametric metric spaces. As a consequence, we deduce fixed point theorems for ( α , ψ ) $(\alpha , \psi )$ -rational-type contractive mappings in partially ordered rectangular generalized fuzzy metric spaces.

In this manuscript, we introduce the concept of intuitionistic fuzzy controlled metric-like spaces via continuous t-norms and continuous t-conorms. This new metric space is an extension to intuitionistic fuzzy controlled metric-like spaces, controlled metric-like spaces and controlled fuzzy metric spaces, and intuitionistic fuzzy metric spaces. We prove some fixed-point theorems and we present non-trivial examples to illustrate our results. We used different techniques based on the properties of the considered spaces notably the symmetry of the metric. Moreover, we present an application to non-linear fractional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we define asymptotic dimension of fuzzy metric spaces in the sense of George and Veeramani. We prove that asymptotic dimension is an invariant in the coarse category of fuzzy metric spaces. We also show several properties of asymptotic dimension in the fuzzy setting which resemble the properties of asymptotic dimension in the metric setting. We finish with calculating asymptotic dimension of a few fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

Gated sets in metric spaces play an important role in the study of convexity. In this paper, we investigate the notion of gated sets in the context of betweenness of fuzzy metric spaces. For this purpose, we analyze the validity of postulates presented by Huntington and Kline to the betweenness in GV fuzzy metric spaces. The postulates are different from the usual properties of metric betweenness, amounting to thirteen. Interestingly, the validity of most of these postulates to the betweenness need to be considered in fuzzy normed spaces. In particular, two of the postulates for this relation are valid when the space is 1-dimensional. Five of the postulates for this relation are centrally studied in connection with strict convexity. As a consequence, several characterizations on strict convexity in a GV fuzzy normed space under the minimum t-norm are established. [ABSTRACT FROM AUTHOR]

In this paper, the results of a quadruple coincidence point (QCP) are established for commuting mapping in the setting of fuzzy metric spaces (FMSs) without using a partially ordered set. In addition, several related results are presented in order to generalize some of the prior findings in this area. Finally, to support and enhance our theoretical ideas, non-trivial examples and applications for finding a unique solution for Lipschitzian and integral quadruple systems are discussed. [ABSTRACT FROM AUTHOR]

Some fixed point theorems are developed in fuzzy metric spaces using an altering distance function under binary relationship. We ensure the existence and uniqueness of the solution to ordinary differential equation using our results. We also give a non-trivial example to illustrate our primary result. Our results strengthen and extend the Theorem 3.1 of Shen et al. (Applied Mathematics Letters, 25 (2012), 138-141).

In this article, the concept of fuzzy (σ , Z) -contractive mappings is introduced in the setting of fuzzy metric spaces. Thereafter, we utilize our newly introduced concept to prove some existence and uniqueness theorems in M -complete fuzzy metric spaces. Our obtained theorems extend and generalize the corresponding results in the existing literature. Moreover, some examples are adopted to exhibit the utility of the newly obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce Θf-type controlled fuzzy metric spaces and establish some fixed point results in this spaces. We provide suitable examples to validate our result. We also employ an application to substantiate the utility of our established result for finding the unique solution of an integral equation emerging in the dynamic market equilibrium aspects to economics. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of extended modular S-metric spaces which induce the notion of extended fuzzy S-metric spaces and is a generalization of some classes of metric type spaces. We obtain some results for JS-Prešić contractive mappings in this new setting and in the related fuzzy setting. In fact, we obtain the Prešić fixed points via an easier way than the previous methods. An application in integral equations will support our results. [ABSTRACT FROM AUTHOR]

We present a sequence of sets converging, under suitable conditions and respect to the Hausdorff intuitionistic fuzzy metric, to the attractor set of certain intuitionistic fuzzy iterated function systems. For this goal, we will introduce a fuzzy version of the so called α-dense curves which have been used by the author to approximate, with arbitrarily small and controlled error, the attractor set of certain (metric) iterated function systems. In this way, we relate the above mentioned concepts of the intuitionistic fuzzy metric spaces with the α-density theory. [ABSTRACT FROM AUTHOR]

We introduce the definitions of expansivity and topological stability for homeomorphisms on fuzzy metric spaces. We show some basic properties of fuzzy expansive homeomorphisms. Moreover we prove Walters's theorem in the context of fuzzy metric spaces, i.e., a fuzzy expansive system with the fuzzy shadowing property is fuzzy topologically stable. [ABSTRACT FROM AUTHOR]

In this study temporal intuitionistic fuzzy metric space is defined to obtain a dynamic measure that expresses distances between the spatio-temporal points whose positions change over time and also between the data represented by these points. In order to define this new approach, the concepts of temporal fuzzy t-norm, temporal fuzzy t-conorm and temporal fuzzy negation, which do not exist in the literature, are defined and some basic features of these concepts are examined. The concept of temporal intuitionistic fuzzy metric spaces is defined with a new approach on the basis of the idea that the degrees of nearness and non-nearness change over time. On the other hand, the fundamental topological properties of temporal intuitionistic fuzzy metric space are also examined. We show that the fundamental properties provided by classical and fuzzy metric spaces are also preserved by this new temporal metric space. Thus, a new and more general and more dynamic metric topology is obtained, in which the basic topological properties of fuzzy and intuitionistic fuzzy metric spaces are preserved. [ABSTRACT FROM AUTHOR]

Fixed point theory in fuzzy metric spaces plays very important role in theory of nonlinear problems in applied science. In this paper, we prove an existence result of common fixed point of four nonlinear mappings satisfying a new type of contractive condition in a generalized fuzzy metric space, called weak non-Archimedean fuzzy metric space. Our main results can be applied to solve the existence of solutions of non-linear equations in fuzzy metric spaces. Some examples supporting our main theorem are also given. Our results improve and generalize some recent results contained in Vetro (2011)[16]to generalized contractive conditions under some suitable conditions and many known results in the literature.

We introduce the notion of generalized parametric metric spaces along with the study of its various properties. Further, we prove some new fixed point theorems for (α , ψ) -rational-type contractive mappings in generalized parametric metric spaces. As a consequence, we deduce fixed point theorems for (α , ψ) -rational-type contractive mappings in partially ordered rectangular generalized fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, the completion of fuzzy normed linear space (in the sense of Bag and Samanta) is studied. First, some properties of convergence fuzzy point sequences are discussed. Specially, we give another characterisation of Q-neighbourhood base of θ λ (λ ∈ (0 , 1 ]) for I-topology introduced by Saheli. Then we show that each fuzzy normed linear space has an (up to isomorphism) unique complete fuzzy normed linear space which contains an uniformly dense in every stratum subspace isomorphic to it. [ABSTRACT FROM AUTHOR]

In the present work we solve the problem of finding the fuzzy distance between two subsets of a fuzzy metric space for which we use a non-self fuzzy contraction mapping from one set to the other. It is a fuzzy extension of the proximity point problem which is by its nature a problem of global optimization. The contraction is defined here by two control functions. We define a geometric property of the fuzzy metric space. The main result is illustrated with an example. Our result extends a fuzzy version of the Banach contraction mapping principle.

In this paper, we introduce the notion of fuzzy bipolar metric space and prove some fixed point results in this space. We provide some non-trivial examples to support our claim and also give applications for the usability of the main result in fuzzy bipolar metric spaces. [ABSTRACT FROM AUTHOR]

We introduce the notion of fuzzy degree of nondensifiability (FDND for short) as a non-negative real number that measures the Hausdorff distance between a bounded set of a fuzzy metric space and its closest Peano continuum. The FDND allows us to analyze the precompact subsets of a fuzzy metric space. In fact, we present a characterization of the family of precompact and arc-connected subsets in terms of the FDND, namely, those subsets whose FDND is equal to zero, provided that the fuzzy metric space be of stationary type. As an application of our results, we prove a variant of the Sadovskiĭ fixed point theorem based on the FDND, which generalizes that of Schauder in fuzzy Banach spaces. Likewise, we present an example where the FDND method is applicable but the one based on measures of noncompactness is not. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new concepts, generalized α-η-FZ-contraction and modified α-η-FZ-contraction, which unify several types of contractions in the context of fuzzy metric spaces. We discuss the existence and uniqueness results of such mappings in the setting of a complete fuzzy metric space in the sense of George and Veeramani and present several significant consequences of our obtained results by using variant examples for FZ-simulation functions and admissible mappings. Some examples are provided to illustrate the usability of our main results.

In this paper, first we discuss the variants of the weakly commuting and compatible mappings in the context of coupled fixed point theory of fuzzy metric spaces. Secondly, we investigate the existence and uniqueness of the common fixed point for pairs of weakly compatible mappings satisfying a new contraction condition in the setup of fuzzy metric spaces with Had i type t-norm . Further, we talk about some results for the variants of weakly commuting and compatible mappings. At the end, as an application, we obtain metrical version of the discussed results.

A new distance metric between interval-valued fuzzy sets is proposed. The four special logic metric spaces based on the distance are structured. we analysis and compare the structures of the four logic metric spaces. It is shown that the Łukasiewicz logic metric space and Goguen logic metric space are more suitable for interval-valued fuzzy reasoning. Moreover, the robustness of interval-valued fuzzy reasoning triple I methods are studied in the two logic metric spaces. We prove that fuzzy reasoning triple I methods based on the interval-valued Łukasiewicz residuated implication and interval-valued Goguen residuated implication are robust. [ABSTRACT FROM AUTHOR]

A new distance metric between interval-valued fuzzy sets is proposed. The four special logic metric spaces based on the distance are structured. we analysis and compare the structures of the four logic metric spaces. It is shown that the Łukasiewicz logic metric space and Goguen logic metric space are more suitable for interval-valued fuzzy reasoning. Moreover, the robustness of interval-valued fuzzy reasoning triple I methods are studied in the two logic metric spaces. We prove that fuzzy reasoning triple I methods based on the interval-valued Łukasiewicz residuated implication and interval-valued Goguen residuated implication are robust. [ABSTRACT FROM AUTHOR]

Fixed point theory in fuzzy metric spaces plays very important role in theory of nonlinear problems in applied science. In this paper, we prove an existence result of common fixed point of four nonlinear mappings satisfying a new type of contractive condition in a generalized fuzzy metric space, called weak non-Archimedean fuzzy metric space. Our main results can be applied to solve the existence of solutions of non-linear equations in fuzzy metric spaces. Some examples supporting our main theorem are also given. Our results improve and generalize some recent results contained in Vetro (2011) [16] to generalized contractive conditions under some suitable conditions and many known results in the literature. [ABSTRACT FROM AUTHOR]

Inspired by the work of Dakjum et al. [Eshi, D., Das, P. K. and Debnath, P., Coupled coincidence and coupled common fixed point theorems on a metric space with a graph, Fixed Point Theory Appl., 37 (2016), 1-14], we introduce a new class of G-f-contraction mappings in complete fuzzy metric spaces endowed with a directed graph and prove some existence results for coupled coincidence and coupled common fixed point theorems of this type of contraction mappings in complete fuzzy metric spaces endowed with a directed graph. [ABSTRACT FROM AUTHOR]

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This article is the forward result of α-admissible and (α,ψ)-contractive mappings in fuzzy metric spaces. We establish new theorem for such contractions to find fixed point in fuzzy metric space. Our Theorem is generalizations of some interesting outputs in metric spaces. Moreover, an example and application to ordinary di¤erential equations are also elaborated to verify the result of the theorem. [ABSTRACT FROM AUTHOR]

In this paper, we state and prove some common fixed point theorems in fuzzy metric spaces. These theorems generalize and improve known results (see [1]).

In this paper, we introduce and prove some classes of fuzzy contractive mappings with altering distance function via α and βκ-admissible mappings in the fuzzy metric spaces. We also give some example and graph which demonstrate the validity of the hypotheses of our main results. Our results improve and extend several previously known fixed point theorems of the existing literature. As an application to our main result a fixed point for contraction mappings of integral type in fuzzy metric spaces are presented. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the existence problems of fixed points for multi-valued mappings and minimization theorems in fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

In the paper, an arclength notion of continuous curves in fuzzy metric spaces is proposed, and some arclength properties are studied, including invariance, additivity, continuity and boundedness. It turns out that these arclength properties imply the corresponding ones in metric spaces. [ABSTRACT FROM AUTHOR]