New fixed figure results with the notion of k-ellipse

In this paper, as a geometric approach to the fixed-point theory, we prove new fixed-figure results using notion of k-ellipse on metric space. For purpose, are inspired by Caristi type mapping, Kannan contraction, Chatterjea contraction and Ćirić contraction. After that, give some existence uniqueness theorems fixed k-ellipse. We also support our obtained with illustrative examples. Finally, present application S-Shaped Rectified Linear Activation Unit (SReLU) show importance theoretical results.