Common fixed point theorems in C*-algebra-valued b-metric spaces endowed with a graph and applications

TL;DR

This paper develops common fixed point theorems in C*-algebra-valued b-metric spaces with graphs, providing examples and applications to operator and integral equations.

Contribution

It introduces fixed point results in a new setting of C*-algebra-valued b-metric spaces with graphs, extending existing theories.

Findings

Established fixed point theorems in the new space setting

Provided examples illustrating the main results

Applied results to solve operator and integral equations

Abstract

In this paper, we equip a C*-algebra-valued b-metric spaces with a graph G = (V,E) and establish some common fixed point theorems. Also, some examples in support of our main results are provided. Finally, as applications, existence and uniqueness of solution for a type of operator equation and an integral equation are discussed.