Geometric Properties of Fixed Points and Simulation Functions

TL;DR

This paper explores the geometric characteristics of fixed point sets in metric and generalized metric spaces, focusing on simulation functions to analyze non-unique fixed points and their geometric structures.

Contribution

It introduces the use of simulation functions to study the geometric properties of fixed points in metric, S-metric, and b-metric spaces, highlighting non-uniqueness.

Findings

Fixed point sets can form various geometric figures.

Simulation functions help analyze non-unique fixed points.

Geometric properties vary across different types of metric spaces.

Abstract

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.