Common Fixed Point Theorems in Fuzzy Metric Space with Applications

TL;DR

This paper introduces new fixed point theorems in fuzzy metric spaces using implicit functions and integral-type contractions, with applications to functional equations and supporting examples.

Contribution

It presents novel fixed point theorems in fuzzy metric spaces employing implicit functions and integral contractions, extending existing theories.

Findings

Established new fixed point theorems in fuzzy metric spaces.

Applied the theorems to systems of functional equations.

Provided an example demonstrating the results.

Abstract

In this paper, we introduce a new class of implicit function to prove common fixed point theorems in fuzzy metric space. Moreover we define a new altering distance in terms of integral and utilize the same to deduce integral type contractive conditions. Secondly we present application of main results to the system of functional equations. At the end we give an example in support of results of the paper.