# Topological and geometric approach to the fixed-point theory with leakly rectified linear unit application Topological and geometric approach to the fixed-point theory

## Main Article Content

## Abstract

In this paper, we focus on the Banach contraction principle on $S_{b}$-metric spaces. At first, we give a brief history of the fixed-point theory and recall some necessary notions related to $S_{b}$-metric spaces. We present an alternative proof to the Banach contraction principle on $S_{b}$-metric spaces. Also, we investigate some geometric properties of the fixed-point set of a given self-mapping modifying the Banach contractive condition with an illustrative example. Finally, we obtain an application to Leakly rectified linear unit activation functions.

## Article Details

How to Cite

Taş, N.
(2023).
Topological and geometric approach to the fixed-point theory with leakly rectified linear unit application.

*Acta Mathematica Universitatis Comenianae, 92*(1), 91-100. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1877/977
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