On Fixed Points in the Setting of $C^*$-Algebra-Valued Controlled $F_c$-Metric Type Spaces

TL;DR

This paper introduces C*-algebra-valued controlled Fc-metric type spaces as a generalization of F-cone metric spaces and establishes fixed point theorems within this framework, supported by an illustrative example.

Contribution

It extends fixed point theory to a new class of metric spaces valued in C*-algebras, broadening the scope of metric space analysis.

Findings

Proved fixed point theorems under various contractive conditions.

Established the structure of C*-algebra-valued controlled Fc-metric type spaces.

Provided an example demonstrating the applicability of the theorems.

Abstract

In the present article, we first examine the conception of C*-algebra-valued controlled Fc-metric type spaces as a generalization of F-cone metric spaces over banach algebra. Further, we prove some fixed point theorem with different contractive conditions in the framework of C*-algebra-valued controlled Fc-metric type spaces. Secondly, we furnish an example by means of the acquired result.