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

Abstract

Based on the concept and properties of $C^{\ast }$-algebras, the paper introduces a concept of $C_{\ast }$-class functions. Then by using these functions in $C^{\ast }$-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.

18 pages