Report
New Fixed Figure Results with the Notion of $k$-Ellipse
| العنوان: | New Fixed Figure Results with the Notion of $k$-Ellipse |
|---|---|
| المؤلفون: | Taş, Nihal, Aytimur, Hülya, Güvenç, Şaban |
| المصدر: | Mathematica Moravica, vol. 27, no. 1, pp. 37-52, Jan. 2023 |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, 54H25, 47H09, 47H10 |
| الوصف: | 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 \'{C}iri\'{c} 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. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.5937/MatMor2301037A |
| URL الوصول: | http://arxiv.org/abs/2112.10204 |
| رقم الانضمام: | edsarx.2112.10204 |
| قاعدة البيانات: | arXiv |
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