Fixed point results for set-contractions on semi-metric space with a directed graph

TL;DR

This paper establishes fixed point theorems for set-contractions in semi-metric spaces with directed graphs, broadening the scope of existing fixed point results in such spaces.

Contribution

It introduces generalized rational contractive mappings in semi-metric spaces with directed graphs, extending and improving previous fixed point theorems.

Findings

Fixed point results for generalized rational contractive mappings.

Examples illustrating the theorems.

Extension of existing fixed point theorems.

Abstract

Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and generalize many results in the existing literature.