Application to Activation Functions through Fixed-Circle Problems with Symmetric Contractions

Author:

Anjum Rizwan1ORCID,Abbas Mujahid2,Safdar Hira1,Din Muhammad3ORCID,Zhou Mi4ORCID,Radenović Stojan5ORCID

Affiliation:

1. Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, Pakistan

2. Department of Mathematics, Government College University, Katchery Road, Lahore 54000, Pakistan

3. Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan

4. Center for Mathematical Research, University of Sanya, Sanya 572022, China

5. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia

Abstract

In this paper, our main aim is to present innovative fixed-point theorems that provide solutions to the fixed-circle problem with symmetric contractions. We accomplish this by employing operator enrichment techniques within the context of Banach spaces. Furthermore, we demonstrate the practical application of these theorems by showcasing their relevance to the rectified linear unit (ReLU) activation function. By exploring the connection between fixed points and activation functions, our work contributes to a deeper understanding of the behavior and properties of these fundamental mathematical concepts.

Funder

Key Research and Development Project of Hainan Province

High-Level Project of Hainan Provincial Natural Science Foundation

Sanya City Science and Technology Innovation Special Project

Key Special Project of University of Sanya

Publisher

MDPI AG

Reference29 articles.

1. Some fixed-circle theorems on metric spaces;Bull. Malays. Math. Sci. Soc.,2019

2. On the Fixed Circle Problem on Metric Spaces and Related Results;Mlaiki;Axioms,2023

3. Taş, N., Özgür, N.Y., and Mlaiki, N. (2018). New types of Fc-contractions and the fixed-circle problem. Mathematics, 6.

4. New fixed-circle results on S-metric spaces;Bull. Math. Anal. Appl.,2017

5. Fixed-circle problem on S-metric spaces with a geometric viewpoint;Facta Univ. (NIS) Ser. Math. Inform.,2019

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1. Certain Fixed Point Results via Contraction Mappings in Neutrosophic Semi-Metric Spaces;Journal of Advances in Applied & Computational Mathematics;2024-08-14

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