Geometric Properties of Fixed Points and Simulation Functions

Geometric properties of the fixed point set $Fix(f)$ of a self-mapping $f$ on a metric or a generalized metric space is an attractive issue. The set $Fix(f)$ can contain a geometric figure (a circle, an ellipse, etc.) or it can be a geometric figure. In this paper, we consider the set of simulation functions for geometric applications in the fixed point theory both on metric and some generalized metric spaces ($S$-metric spaces and $b$-metric spaces). The main motivation of this paper is to investigate the geometric properties of non unique fixed points of self-mappings via simulation functions.