Topological and geometric approach to the fixed-point theory with leakly rectified linear unit application Topological and geometric approach to the fixed-point theory

Abstract

In this paper, we focus on the Banach contraction principle on $S_{b}$-metric spaces. At first, we give a brief history of the fixed-point theory and recall some necessary notions related to $S_{b}$-metric spaces. We present an alternative proof to the Banach contraction principle on $S_{b}$-metric spaces. Also, we investigate some geometric properties of the fixed-point set of a given self-mapping modifying the Banach contractive condition with an illustrative example. Finally, we obtain an application to Leakly rectified linear unit activation functions.