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

TL;DR

This paper investigates fixed point theorems for set-contractions within dislocated metric spaces equipped with a directed graph, extending existing results and demonstrating well-posedness with illustrative examples.

Contribution

It introduces new fixed point results for set-contractions in dislocated metric spaces with directed graphs, broadening the scope of prior fixed point theories.

Findings

Fixed point theorems for set-contractions established.

Examples illustrating the main results provided.

Results extend existing fixed point literature.

Abstract

Generalized (rational) graph contractions in the framework of a dislocated metric space endowed with a directed graph are investigated. Fixed point results for set-contractions are obtained. We also provide some examples to illustrate our main results. Moreover, the well-posedness of obtained fixed point results are also shown. Our obtained results extend many results in the existing literature.