Geometric properties of fixed points and simulation functions

Abstract

The main motivation of this paper is to investigate the geometric properties of non unique fixed points of self-mappings via 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).