“A Study Of Some Fixed Point Theorems And Their Application In Fuzzy Metric Spaces”

Abstract

In this the research work deals mainly with fixed point theorems and their applications. The fuzzy topological spaces and quasi fuzzy metric spaces are introduced. Also, the variational principle and Christi’s fixed point theorem in fuzzy topological spaces are established, the results of which are utilized to obtain a fixed point theorem for Manger probabilistic metric space. The compatible pair of reciprocally continuous mappings is defined and a fixed point theorem in a fuzzy metric space is obtained which generates a fixed point but does not force the map to be continuous. Further, V|/-compatible mapping is introduced in a fuzzy metric space and established the altering distances between the points using certain control functions which differ from the previous works. R-weakly commuting of type (A„) and non compatible mappings in fuzzy metric space are introduced which leads to the proof of fixed point theorem without assuming completeness of the space or continuity.