Uniqueness of coincidence and common fixed points in fuzzy b-metric spaces with applications to integral equations

Abstract

This paper investigates the existence of coincident points and common fixed points for two self-mappings in a fuzzy b-metric space. We establish that under the conditions of weak compatibility and suitable contractive criteria, these mappings possess a unique common fixed point. Illustrative examples are provided to demonstrate the validity of our results, along with an application to determine the unique solution of an integral equation. The application underscores the practical relevance of our findings, particularly in addressing conditions for dynamic market equilibrium in economics.