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.
Categories: math.FA