$\varphi-$fixed point theorems in $C^{\ast}-$algebra valued partial metric spaces

TL;DR

This paper establishes new fixed point theorems for mappings in $C^{ ext{*}}$-algebra valued (partial) metric spaces, extending existing results with concrete examples.

Contribution

It introduces $ ext{phi}$-fixed point theorems in $C^{ ext{*}}$-algebra valued partial metric spaces, a novel extension in the fixed point theory domain.

Findings

Proved existence of $ ext{phi}$-fixed points in $C^{ ext{*}}$-algebra valued metric spaces.

Derived fixed point theorems in $C^{ ext{*}}$-algebra valued partial metric spaces.

Provided examples supporting the theoretical results.

Abstract

In this present article, we etablish some existence results of $\varphi-$fixed point of a mapping in a $C^{\ast}$-algebra valued metric spaces and we deduce some fixed point theorems in $C^{\ast}$-algebra valued partial metric spaces. Non-trivial examples are further provided to support the hypotheses of our results.