Common Fixed Points of Weakly Commuting Multivalued Mappings on Domain of Sets Endowed with Directed Graph

TL;DR

This paper establishes the existence of common fixed points for multivalued mappings on graph-endowed sets under contraction conditions, extending and unifying previous fixed point results without requiring continuity.

Contribution

It introduces new fixed point theorems for multivalued mappings with graphic contraction conditions, broadening the scope of fixed point theory in graph-structured domains.

Findings

Existence of coincidence points and common fixed points proved.

Results apply to multivalued mappings without continuity assumptions.

Examples demonstrate the applicability of the theorems.

Abstract

In this paper, the existence of coincidence points and common fixed points for multivalued mappings satisfying certain graphic {\psi}-contraction contractive conditions with set-valued domain endowed with a graph, without appealing to continuity, is established. Some examples are presented to support the results proved herein. Our results unify, generalize and extend various results in the existing literature.