Common fixed points for $C^{*}$-algebra-valued modular metric spaces via $C_{*}$-class functions with application

TL;DR

This paper introduces $C_{*}$-class functions within $C^{*}$-algebra-valued modular metric spaces and establishes new common fixed point theorems, with an application to integral equations.

Contribution

It defines $C_{*}$-class functions and applies them to prove fixed point theorems in $C^{*}$-algebra-valued modular metric spaces, extending previous results.

Findings

Established new fixed point theorems using $C_{*}$-class functions.

Proved existence and uniqueness of solutions for a system of integral equations.

Extended the theory of fixed points in $C^{*}$-algebra-valued metric spaces.

Abstract

Based on the concept and properties of $C^{*}$-algebras, the paper introduces a concept of $C_{*}$-class functions. Then by using these functions in $C^{*}$-algebra- valued modular metric spaces of moeini et al. [14], some common fixed point theorems for self-mappings are established. Also, to support of our results an application is provided for existence and uniqueness of solution for a system of integral equations.