Compatibility of type (P) and fixed point theorem in fuzzy metric spaces

Abstract

Fuzzy metric space is first defined by Kramosil and Michalek in 1975. Many authors modified Fuzzy metric space and proved fixed point results in Fuzzy metric space. Singh B. and Chauhan were first introduced the concept of compatible mappings of Fuzzy metric space and proved the common fixed point theorem in 2000. Cho et al were introduced the concept of compatible mapping of type (P). In this paper, a fixed point theorem for six self-mappings is presented by using the concept of compatible maps of type (P) which is the generalized result.