Fixed k-cassini oval results on metric spaces

Abstract

In this paper, we generalize the well-known Cassini curves to metric spaces by introducing the concept of k-Cassini ovals. We provide various examples of k-Cassini ovals in different metric spaces, accompanied by illustrative shapes. Furthermore, we present the existence and uniqueness theorems for the transformation T : X → X, establishing conditions under which T preserves the k-Cassini oval within the metric space (X, d). Finally, we demonstrate an application of this framework to the LReLU (Leaky Rectified Linear Unit) function.