Fixed-Circle Problem on S-Metric Spaces with a Geometric Viewpoint

TL;DR

This paper explores the fixed-circle problem within S-metric spaces, establishing conditions for the existence and uniqueness of fixed circles and providing illustrative examples.

Contribution

It introduces the fixed-circle problem to S-metric spaces and develops new existence and uniqueness results for fixed circles in this context.

Findings

Established conditions for fixed circle existence

Proved uniqueness of fixed circles under certain conditions

Provided examples of self-mappings with fixed circles

Abstract

Recently, a new geometric approach which is called the fixed-circle problem has been gained to fixed-point theory. The problem is introduced and studied using different techniques on metric spaces. In this paper, we consider the fixed-circle problem on $S$-metric spaces. We investigate existence and uniqueness conditions for fixed circles of self-mappings on an $S$-metric space. Some examples of self-mappings having fixed circles are also given.