Bilateral-type solutions to the fixed-circle problem with rectified linear units application

Abstract

In this paper, we prove new fixed-circle (resp. fixed-disc) results using the bilateral type contractions on ametric space. To do this, we modify some known contractive conditions called the Jaggi-type bilateral contraction andthe Dass-Gupta type bilateral contraction. We give some examples to show the validity of our obtained results. Also,we construct an application to rectified linear units activation functions used in the neural networks. This applicationshows the importance of studying “fixed-circle problem”.