Some common fixed point theorems in fuzzy metric spaces

Abstract

The aim of this paper is to prove some common fixed point theorems in (GV)-fuzzy metric spaces.While proving our results, we employed the idea of compatibility due to Jungck [14] together with subsequentially continuity due to Bouhadjera and Godet-Thobie [4] respectively (also alternately reciprocal continuity due to Pant [28] together with subcompatibility due to Bouhadjera and Godet-Thobie [4] as in Imdad et al. [12] wherein conditions on completeness of the underlying space (or subspaces) together with conditions on continuity in respect of any one of the involved maps are relaxed. Our results substantially generalize and improve a multitude of relevant common fixed point theorems of the existing literature in metric as well as fuzzy metric spaces which include some relevant results due to Imdad et al.[10], Mihet [18], Mishra [19], Singh [28] and several others.