Unified fixed point theorems for mappings in fuzzy metric spaces via implicit relations

Abstract

Abstract In this paper, we prove some fixed point theorems for weakly compatible mappings in fuzzy metric spaces employing common limit range property with implicit relations. We also furnish some illustrative examples to support our main results. As an application to our main result, we derive a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results including the ones contained in the paper of Gopal et al. (2011).