Best Proximity Point Theorems for Single and Multivalued Mappings in Fuzzy Multiplicative Metric Space

In this paper, we introduce fuzzy multiplicative metric space and prove some best proximity point theorems for single-valued and multivalued proximal contractions on the newly introduced space. As corollaries of our results, we prove some fixed-point theorems. Also, we present best proximity point theorems for Feng-Liu-type multivalued proximal contraction in fuzzy metric space. Moreover, we illustrate our results with some interesting examples.

Extended Rectangular Fuzzy B-metric Space

In this paper, we introduce an extended rectangular fuzzy b-metric space which generalizes rectangular fuzzy b-metric space and rectangular fuzzy metric space. We show that an extended rectangular fuzzy b-metric space is not Hausdorff. A Banach fixed point theorem is proved as a special case of our main result where a Ciric type contraction was employed. Our main result generalizes some comparable results in rectangular fuzzy b-metric space and rectangular fuzzy metric space. We provide some examples to support the concepts and results presented herein. As an application of our result, we obtain the existence of the solution of the integral equation.

The periodic points of ε-contractive maps in fuzzy metric spaces

<p>In this paper, we introduce the notion of ε-contractive maps in fuzzy metric space (X, M, ∗) and study the periodicities of ε-contractive maps. We show that if (X, M, ∗) is compact and f : X −→ X is ε-contractive, then P(f) = ∩ ∞n=1f n (X) and each connected component of X contains at most one periodic point of f, where P(f) is the set of periodic points of f. Furthermore, we present two examples to illustrate the applicability of the obtained results.</p>

Common Fixed Point Theorems in Fuzzy Metric Space

In the present paper we prove common fixed point theorem for occasionally weakly compatible mapping in fuzzy metric space. The theorem is a version of many fixed point theorem in fuzzy metric spaces, given by many authors announced in the literature.

Generalized fuzzy GV-Hausdorff distance in GFGV-fractal spaces with application in integral equation

We propose a method for constructing a generalized fuzzy Hausdorff distance on the set of the nonempty compact subsets of a given generalized fuzzy metric space in the sence of George–Veeramni and Tian–Ha–Tian. Next, we define the generalized fuzzy fractal spaces. Morever, we obtain a fixed point theorem of a class of generalized fuzzy contractions and present an application in integranl equation.

The Strong Laws of Large Numbers for Set-Valued Random Variables in Fuzzy Metric Space

In this paper, we firstly introduce the definition of the fuzzy metric of sets, and discuss the properties of fuzzy metric induced by the Hausdorff metric. Then we prove the limit theorems for set-valued random variables in fuzzy metric space; the convergence is about fuzzy metric induced by the Hausdorff metric. The work is an extension from the classical results for set-valued random variables to fuzzy metric space.

sp− Closedness and sp − Convergent Sequences in Intuitionistic Fuzzy Metric Space

The aim of present article is to introduce the concepts of sp– convergent sequence in intuitionistic fuzzy metric spaces and analyze relations of convergence, sp– convergence, s∞– convergence and st– convergence in intuitionistic fuzzy metric spaces. Further, we examine sp– convergence, s∞– convergence and st– convergence using the subsequence of convergent sequence in intuitionistic fuzzy metric spaces. Stationary intuitionistic fuzzy metric spaces are defined and investigated. We Finally define sp– closed sets, s∞– closed sets and st– closed sets in intuitionistic fuzzy metric spaces and investigate relations of them.