New fixed point theorems for nonlinear contractive mappings of integral type involving $\omega$-distance and its applications

Abstract

This paper introduces a new class of contractive mappings of integral type involving the concept of $\omega$-distance in complete metric spaces. We establish a fixed point theorem for these mappings, providing sufficient conditions for the existence and uniqueness of fixed points. We also provide an example to illustrate the validity of our results and discuss applications of this fixed point theorem in solving integral equations, demonstrating its practical relevance.