Some remarks and corrections of recent resultsfrom the framework of $S$-metric spaces

Nora Fetouci^a, Stojan Radenović<sup>b

a</sup> LMPA Laboratory, Department of Mathematics, Jijel University, Jijel, Algeria
^b Faculty of Mechanical Engineering, University of Belgrade, Belgrad, Serbia

Abstract: The content of this paper consists of results on Wardowski's $F$-contraction within $S$-metric spaces. Namely, in it we present corrections to some recent results by using only the property $\mathrm{F1}$ of strict increasing of the function $F$. In our results, we combine $\beta $-admissible functions with $ F$-contractions. Finally, we give an example that shows that $F$-contraction in the framework of $S$-metric spaces is a true generalization of Banach's contraction principle in the same framework.

Keywords: $S$-metric space, $b$-metric space, fixed point, $F$-contraction, $\beta$-admissible.

UDC: 515.124

Received: 09.10.2024
Received in revised form: 23.12.2024
Accepted: 24.02.2025

Language: English