C* -algebra-valued Sb-metric spaces and applications to integral equations

Abstract

We first introduce the concept of $C^{*}$-algebra-valued $S_{b}$-metric space, then we prove Banach contraction principle in this space. Finally, existence and uniqueness results for one type of integral equation is discussed.

Keywords

• banach contraction principle
• $b$-metric space
• $s_{b}$-metric space
• $c^*$-algebra
• integral equation