Ellipses and similarity transformations with norm functions

Özgür, Nihal Yılmaz

doi:10.3906/mat-1806-22

Cited by 2 publications

(1 citation statement)

References 8 publications

(19 reference statements)

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“…Example 2.4 in [24]). The circle C 0,1 is seen in the following figure which is drawn using Mathematica [31].…”

Section: Introductionmentioning

confidence: 99%

New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces

Mlaiki,

Ozgur,

Tas

2021

Preprint

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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.

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“…Example 2.4 in [24]). The circle C 0,1 is seen in the following figure which is drawn using Mathematica [31].…”

Section: Introductionmentioning

confidence: 99%

New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces

Mlaiki,

Ozgur,

Tas

2021

Preprint

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On the Fixed Circle Problem on Metric Spaces and Related Results

Mlaiki

Özgür

Taş

et al. 2023

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The fixed-circle issue is a geometric technique that is connected to the study of geometric characteristics of certain points, and that are fixed by the self-mapping of either the metric space or of the generalized space. The fixed-disc problem is a natural resultant that arises as a direct outcome of this problem. In this study, our goal is to examine new classes of self-mappings that meet a new particular sort of contraction in a metric space. The common geometrical characteristic of the set of fixed points of any element of these classes is that a circle or even a disc, that is either termed the fixed circle or even the fixed disc of the appropriate self-map, is included within that set. In order to accomplish this, we establish two new classifications of contraction mapping: Fc-contractive mapping and Fc-expanding mapping. In the investigation of neural networks, activation functions with either fixed circles (or even fixed discs) are observed frequently. This demonstrates how successful our results with the fixed-circle (respectively, the fixed-disc) model were.

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Ellipses and similarity transformations with norm functions

Cited by 2 publications

References 8 publications

New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces

New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces

On the Fixed Circle Problem on Metric Spaces and Related Results

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