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New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
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Abstract
- The fixed-circle problem is a recent problem about the study of geometric properties of the fixed point set of a self-mapping on metric (resp. generalized metric) spaces. The fixed-disc problem occurs as a natural consequence of this problem. Our aim in this paper, is to investigate new classes of self-mappings which satisfy new specific type of contraction on a metric space. We see that the fixed point set of any member of these classes contains a circle (or a disc) called the fixed circle (resp. fixed disc) of the corresponding self-mapping. For this purpose, we introduce the notions of an $F_{c}$-contractive mapping and an $F_{c}$-expanding mapping. Activation functions with fixed circles (resp. fixed discs) are often seen in the study of neural networks. This shows the effectiveness of our fixed-circle (resp. fixed-disc) results. In this context, our theoretical results contribute to future studies on neural networks.<br />Comment: 15 pages, 1 figure
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....4b7d67d274e7dbca8ed03421a4eb531f
- Full Text :
- https://doi.org/10.48550/arxiv.2101.10770