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- W3126049054 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." @default.
- W3126049054 created "2021-02-01" @default.
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- W3126049054 date "2021-01-26" @default.
- W3126049054 modified "2023-10-18" @default.
- W3126049054 title "New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces" @default.
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