IMPLICIT RELATIONS AND THEIR ROLE IN ESTABLISHING FIXED POINT THEOREMS IN FUZZY METRIC SPACES

Abstract

In this paper, we explore the concept of implicit relations and their sig- nificant role in establishing fixed point theorems within the framework of fuzzy metric spaces. We begin by revisiting the fundamental definitions and properties of fuzzy metric spaces, followed by an in-depth analysis of implicit relations. Through this study, we demonstrate how these relations facilitate the establishment of fixed point theorems, particularly in situations where traditional techniques may fall short. The results presented herein extend and generalize several known theorems, thereby broadening the scope of fixed point theory in fuzzy metric spaces.