A Geometric Interpretation to Fixed-Point Theory on $S_{b}$-Metric Spaces

TL;DR

This paper introduces a geometric approach to fixed-point theory in $S_{b}$-metric spaces, defining new contractions and fixed figures like discs and ellipses, with examples validating the results.

Contribution

It proposes a novel geometric interpretation and new contraction types for fixed-point theory in $S_{b}$-metric spaces, extending existing concepts.

Findings

Established fixed-figure theorems for multiple fixed points

Defined new contractions on $S_{b}$-metric spaces

Provided examples demonstrating theoretical results

Abstract

In this paper we present some fixed-figure theorems as a geometric approach to the fixed-point theory when the number of fixed points of a self-mapping is more than one. To do this, we modify the Jleli-Samet type contraction and define new contractions on $S_{b}$-metric spaces. Also, we give some necessary examples to show the validity of our theoretical results. Keywords: Fixed figure, fixed disc, fixed ellipse, fixed hyperbola, fixed Cassini curve, fixed Apollonius circle.