Interpolative generalised Meir-Keeler contraction

Abstract

Introduction/purpose: The aim of this paper is to introduce the notion of an interpolative generalised Meir-Keeler contractive condition for a pair of self maps in a fuzzy metric space, which enlarges, unifies and generalizes the Meir-Keeler contraction which is for only one self map. Using this, we establish a unique common fixed point theorem for two self maps through weak compatibility. The article includes an example, which shows the validity of our results. Methods: Functional analysis methods with a Meir-Keeler contraction. Results: A unique fixed point for self maps in a fuzzy metric space is obtained. Conclusions: A fixed point of the self maps is obtained.