New fixed figure results with the notion of k-ellipse
Mathematica Moravica, Tome 27 (2023) no. 1.

Voir la notice de l'article dans eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 mapping, 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.
Mots-clés : Fixed figure, fixed k-ellipse, metric space, activation function. 
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Hülya Aytimur; Şaban Güvenç; Nihal Taş. New fixed figure results with the notion of k-ellipse. Mathematica Moravica, Tome 27 (2023) no. 1. https://geodesic-test.mathdoc.fr/item/MM3_2023_27_1_a3/