The generalized fixed point theorem in fuzzy metric spaces and its application to an integral equation

Abstract

This paper presents a generalized fixed-point theorem in fuzzy metric spaces using an implicit

relation to unify different contraction types. Based on continuous t-norms, the result extends previous work

and includes corollaries demonstrating its generality. The approach simplifies analysis by eliminating separate

proofs for each contraction type, while an application to integral equations demonstrates its practical utility,

guaranteeing existence and uniqueness of solutions under specific conditions.