Rational Type Fuzzy-Contraction Results in Fuzzy Metric Spaces with an Application

Abstract

This paper aims to introduce the new concept of rational type fuzzy-contraction mappings in fuzzy metric spaces. We prove some fixed point results under the rational type fuzzy-contraction conditions in fuzzy metric spaces with illustrative examples to support our results. This new concept will play a very important role in the theory of fuzzy fixed point results and can be generalized for different contractive type mappings in the context of fuzzy metric spaces. Moreover, we present an application of a nonlinear integral type equation to get the existing result for a unique solution to support our work.

Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

“…They proved some basic properties of the FM-space by using the notion of a fuzzy set on metric space. Many fixed, coupled and TFP results in the setting of FM-space were discussed and obtained, some references in this direction can be found in [22][23][24].…”

Some set-valued and multi-valued contraction results in fuzzy cone metric spaces

“…After that, a number of authors have studied and contributed their ideas to the problems on FM-spaces. Some of their results can be found in [14][15][16][17][18][19][20][21][22][23][24][25] and the references therein.…”

Some New Coupled Fixed-Point Findings Depending on Another Function in Fuzzy Cone Metric Spaces with Application

“…Recently, in 2020, Li et al [23] proved some strongly coupled FP theorems by using cyclic contractive type mappings in complete FM-spaces. Meanwhile Rehman et al [24] presented the concept of rational type contraction mappings and proved some FP theorems in complete FMspaces with an application.…”