Application to Activation Functions through Fixed-Circle Problems with Symmetric Contractions
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 appl...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-01-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/16/1/69 |
| _version_ | 1797342534300598272 |
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| author | Rizwan Anjum Mujahid Abbas Hira Safdar Muhammad Din Mi Zhou Stojan Radenović |
| author_facet | Rizwan Anjum Mujahid Abbas Hira Safdar Muhammad Din Mi Zhou Stojan Radenović |
| author_sort | Rizwan Anjum |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T10:34:22Z |
| format | Article |
| id | doaj.art-5d17755fa9b04099bf51023e829992c8 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-08T10:34:22Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-5d17755fa9b04099bf51023e829992c82024-01-26T18:38:48ZengMDPI AGSymmetry2073-89942024-01-011616910.3390/sym16010069Application to Activation Functions through Fixed-Circle Problems with Symmetric ContractionsRizwan Anjum0Mujahid Abbas1Hira Safdar2Muhammad Din3Mi Zhou4Stojan Radenović5Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, PakistanDepartment of Mathematics, Government College University, Katchery Road, Lahore 54000, PakistanDepartment of Mathematics, Division of Science and Technology, University of Education, Lahore 54770, PakistanAbdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, PakistanCenter for Mathematical Research, University of Sanya, Sanya 572022, ChinaFaculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, SerbiaIn 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.https://www.mdpi.com/2073-8994/16/1/69fixed circlefixed pointsymmetric contractionsactivation functionneural network |
| spellingShingle | Rizwan Anjum Mujahid Abbas Hira Safdar Muhammad Din Mi Zhou Stojan Radenović Application to Activation Functions through Fixed-Circle Problems with Symmetric Contractions Symmetry fixed circle fixed point symmetric contractions activation function neural network |
| title | Application to Activation Functions through Fixed-Circle Problems with Symmetric Contractions |
| title_full | Application to Activation Functions through Fixed-Circle Problems with Symmetric Contractions |
| title_fullStr | Application to Activation Functions through Fixed-Circle Problems with Symmetric Contractions |
| title_full_unstemmed | Application to Activation Functions through Fixed-Circle Problems with Symmetric Contractions |
| title_short | Application to Activation Functions through Fixed-Circle Problems with Symmetric Contractions |
| title_sort | application to activation functions through fixed circle problems with symmetric contractions |
| topic | fixed circle fixed point symmetric contractions activation function neural network |
| url | https://www.mdpi.com/2073-8994/16/1/69 |
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