On the geometry of fixed points for self-mappings on s-metric spaces

Abstract

In this paper, we focus on some geometric properties related to the set Fix(T), the set of all fixed points of a mapping T : X -> X, on an S-metric space (X, S). For this purpose, we present the notions of an S-Pata type x(0)-mapping and an S-Pata Zamfirescu type x(0)-mapping. Using these notions, we propose new solutions to the fixed circle (resp fixed disc) problem. Also, we give some illustrative examples of our main results.