New fixed figure results with the notion of k-ellipse

Abstract

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 Ciri´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.