A Unified Approach to Fixed Points in Fuzzy Metric Spaces

Abstract

In this paper, we delve into the realm of fuzzy metric spaces to establish new fixed point results by leveraging the concepts of compatibility and weak compatibility among six self-mappings. This research extends the foundational work of Singh and Chouhan [13], broadening the scope and applicability of their results on common fixed points within fuzzy metric spaces. Through rigorous analysis and the introduction of novel techniques, we demonstrate the conditions under which these self-maps exhibit fixed points, thereby contributing to the theoretical advancement of fuzzy metric space theory. Our findings not only validate and extend existing results but also open new avenues for further exploration and application in mathematical and computational contexts where fuzziness and metric considerations are pivotal.