FIXED-CIRCLE PROBLEM ON S-METRIC SPACES WITH A GEOMETRIC VIEWPOINT

Abstract

Recently, a new geometric approach called the fixed-circle problem has been introduced to fixed-point theory. The problem has been 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.