Fixed Point Theoreme In C*-Algebras Valued Asymmetric Spaces

TL;DR

This paper introduces the concept of asymmetric metric spaces valued in C*-algebras, defines contractions, and proves fixed point theorems with an application, expanding fixed point theory in non-symmetric algebraic contexts.

Contribution

It develops the theory of fixed points in C*-algebra valued asymmetric metric spaces, a novel framework in fixed point analysis.

Findings

Existence of fixed points under certain contraction conditions

Uniqueness of fixed points in the new setting

Application demonstrating the theory's utility

Abstract

In this work, we introduce the concept of $C^{*}$-algebra valued asymetric metric space, the concept of forward and the concept of backward $C^{*}$ valued asymetric contractions. We discuss the existence and uniqueness of fixed points for a self-mapping defined on a $C^{*}$-algebra valued asymetric, and we give an application.