Existence of fixed points for condensing operators under an integral condition

TL;DR

This paper establishes fixed point existence results for continuous operators in Banach spaces using measure of noncompactness under an integral condition, generalizing Darbo's theorem, with applications to integral equations.

Contribution

It generalizes Darbo's fixed point theorem by incorporating an integral condition with measure of noncompactness for operators in Banach spaces.

Findings

Fixed point existence under integral conditions

Generalization of Darbo's fixed point theorem

Application to solving integral equations

Abstract

Our aim in this paper is to present results of existence of fixed points for continuous operators in Banach spaces using measure of noncompactness under an integral condition. This results are generalization of results given by A. Aghajania and M. Aliaskaria which are generalization of Darbo's fixed point theorem. As application we use these results to solve an integral equations in Banach spaces.