On fixed point theorems in C^∗-algebra valued b-asymmetric metric spaces

Abstract

In this paper, we introduce the notion of $ C^* $-algebra-valued $ b $-asymmetric metric spaces and show several fixed point theorems that improve on a range of recent works in the literature. The $ C^* $-algebra-valued $ b $-asymmetric metric space is illustrated with examples, as well as an application for determining the existence and uniqueness of a solution for a type of matrix equations and integral equation.

Keywords

• c_∗-algebras
• b-asymmetric spaces
• b-forward convergence
• b-backward convergence
• fixed point
• contraction