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...

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Bibliographic Details
Published in:Symmetry (Basel) 2024-01, Vol.16 (1), p.69
Main Authors: Anjum, Rizwan, Abbas, Mujahid, Safdar, Hira, Din, Muhammad, Zhou, Mi, Radenović, Stojan
Format: Article
Language:English
Subjects:
activation function
Banach spaces
fixed circle
fixed point
Fixed points (mathematics)
Mathematical analysis
neural network
Neural networks
Operators (mathematics)
symmetric contractions
Theorems
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Summary: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.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym16010069