Common fixed point theorems in $C^*$-algebra-valued metric spaces

TL;DR

This paper develops new fixed point theorems for pairs of mappings in complete $C^*$-algebra-valued metric spaces under novel contractive conditions, with applications demonstrated.

Contribution

It introduces new coincidence and common fixed point theorems in $C^*$-algebra-valued metric spaces, expanding fixed point theory in this setting.

Findings

Established fixed point theorems under new contractive conditions

Proved theorems in complete $C^*$-algebra-valued metric spaces

Provided applications of the theoretical results

Abstract

In this paper, we establish coincidence fixed point and common fixed point theorems for two mapping in complete $C^*$-algebra-valued metric spaces which satisfy new contractive conditions. Some applications of our obtained results are given.