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

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.

15 pages, 2 figures

References in corpus (1)

• Some fixed-circle theorems on metric spaces

Cited by in corpus (4)

• New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces
• Geometric Properties of Fixed Points and Simulation Functions
• Pata Zamfirescu Type Fixed-Disc Results with a Proximal Application
• New Multivalued Contractions and the Fixed-Circle Problem