Related fixed point results via $\mathit{C_{*}}$-class functions on $C^{*}$-algebra-valued $G_{b}$-metric spaces

Abstract

We initiate the concept of $C^{*}$-algebra-valued $G_{b}$-metric spaces. We study some basic properties of such spaces and then prove some fixed point theorems for Banach and Kannan types via $\mathit{C_{*}}$-class functions. Also, some nontrivial examples are presented to ensure the effectiveness and applicability of the obtained results.

Keywords

• fixed point
• $\mathit{c_{*}}$-class function
• $c^{*}$-algebra-valued $g_{b}$-metric space