Generalized form of fixed-point theorems in generalized Banach algebra relative to the weak topology with an application

TL;DR

This paper develops a generalized fixed point theorem in Banach spaces using weak topology and applies it to fractional integral equations, demonstrating existence results under specific conditions.

Contribution

It introduces a new hybrid fixed point theorem in generalized Banach spaces utilizing measure of weak non-compactness, with applications to fractional integral equations.

Findings

Established a new fixed point theorem in generalized Banach spaces.

Proved existence of solutions for fractional integral equations.

Provided an illustrative example for the theoretical results.

Abstract

In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence results for the solutions under mixed Lipschitz and weakly sequentially continuous conditions. Finally, an example is given to illustrate the result.