Some common fixed point theorems in intuitionistic fuzzy metric spaces

Abstract

This paper is three fold. Firstly, we shall discuss the notions of different variants of R-weakly commuting mappings (R-weakly commuting mappings of type (Ag), R-weakly commuting mapping of type (Af) and R-weakly commuting mapping of type (P)) and E.A. property in intuitionistic fuzzy metric spaces and then provide various examples to reflect upon the distinctiveness among different variants of R-weakly commuting mappings, see for detail in [14]. Secondly, we prove common fixed point theorem using control function and E.A. property along with weakly compatible maps. At the end, we prove a common fixed point theorem for weakly compatible maps in intuitionistic fuzzy metric spaces which generalizes the result of Alaca, Turkoglu and Yildiz [3].Our results extend, generalize and fuzzify several fixed point theorems on metric spaces, Menger spaces, uniform spaces and fuzzy metric spaces.