New Fixed Figure Results with the Notion of $k$-Ellipse
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866916344820137984 |
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| author | Taş, Nihal Aytimur, Hülya Güvenç, Şaban |
| author_facet | Taş, Nihal Aytimur, Hülya Güvenç, Şaban |
| contents | In this paper, as a geometric approach to the fixed-point theory, we prove new fixed-figure results using the notion of $k$-ellipse on a metric space. For this purpose, we are inspired by the Caristi type contraction, Kannan type contraction, Chatterjea type contraction and Ćirić type contraction. After that, we give some existence and uniqueness theorems of a fixed $k$-ellipse. We also support our obtained results with illustrative examples. Finally, we present a new application to the $S$-Shaped Rectified Linear Activation Unit ($SReLU$) to show the importance of our theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_10204 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | New Fixed Figure Results with the Notion of $k$-Ellipse Taş, Nihal Aytimur, Hülya Güvenç, Şaban Metric Geometry 54H25, 47H09, 47H10 In this paper, as a geometric approach to the fixed-point theory, we prove new fixed-figure results using the notion of $k$-ellipse on a metric space. For this purpose, we are inspired by the Caristi type contraction, Kannan type contraction, Chatterjea type contraction and Ćirić type contraction. After that, we give some existence and uniqueness theorems of a fixed $k$-ellipse. We also support our obtained results with illustrative examples. Finally, we present a new application to the $S$-Shaped Rectified Linear Activation Unit ($SReLU$) to show the importance of our theoretical results. |
| title | New Fixed Figure Results with the Notion of $k$-Ellipse |
| topic | Metric Geometry 54H25, 47H09, 47H10 |
| url | https://arxiv.org/abs/2112.10204 |