Fixed Points of Integral Type Contractions in Uniform Spaces with a Graph

TL;DR

This paper extends fixed point theorems to uniform spaces with a graph and an E-distance, providing conditions for existence and uniqueness of fixed points in a more general setting.

Contribution

It generalizes recent metric fixed point theorems to uniform spaces with additional structures like graphs and E-distances.

Findings

Established existence of fixed points under integral type contractions.

Provided sufficient conditions for the uniqueness of fixed points.

Generalized fixed point results beyond metric spaces.

Abstract

In this paper, we discuss the existence of fixed points for integral type contractions in uniform spaces endowed with both a graph and an $E$-distance. We also give two sufficient conditions under which the fixed point is unique. Our main results generalize some recent metric fixed point theorems.