A Common Fixed Point Theorem in Fuzzy Metric Space Using Property (E. A.) and Implicit Relation

Suneel Kumar, Brian Fisher

Abstract

Recently, I. Altun and D. Turkoglu [Commun. Korean Math. Soc. 23 (1) (2008), 111-124] proved two common fixed point theorems for continuous compatible maps of type (\alpha) or (\beta) on a complete fuzzy metric space with an implicit relation. In this paper, our objective is to prove a common fixed point theorem by removing the assumption of continuity, relaxing compatibility to weak compatibility and replacing the completeness of the space with a set of four alternative conditions for functions satisfying an implicit relation in fuzzy metric space. Our result generalizes the result of I. Altun and D. Turkoglu.