Fuzzy fixed point approach to study the existence of solution for Volterra type integral equations using fuzzy Sehgal contraction.

Abstract

In this manuscript, we present a novel concept known as the fuzzy Sehgal contraction, specifically designed for self-mappings defined in the context of a fuzzy metric space. Our primary objective is to explore the existence and uniqueness of fixed points for self-mappings in fuzzy metric space. To support our conclusions, we present a detailed illustrative case that demonstrates the superiority of the convergence obtained with our suggested method to those currently recorded in the literature. Moreover, we provide graphical depictions of the convergence behavior, which makes our study more understandable and transparent. Additionally, we extend the application of our results to address the existence and uniqueness of solutions for Volterra integral equations.