Fixed points for $F$-expanding mappings in the sense of measures of noncompactness

TL;DR

This paper extends fixed point theory for F-expanding mappings using measures of noncompactness, weakening assumptions and removing surjectivity requirements, with applications to integral equations.

Contribution

It introduces new fixed point results for F-expanding mappings via measures of noncompactness, relaxing previous assumptions and including practical examples.

Findings

Established fixed point theorems under weaker conditions

Provided examples illustrating the theory

Applied results to Volterra-integral equations

Abstract

In this article, we model with measures of noncompactness the well-known concept of F-expanding mappings given by Gornicki (Fixed Point Theory Appl 2017, 9 (2016)). Our results are proved by weakening some assumptions on F and without using the surjectivity. Moreover, the paper contains some examples and an application to the Volterra-integral equation.