Fixed Points Theorems for Enriched Non-expansive Mappings in Geodesic Spaces

Abstract

The purpose of this paper is to extend a class of enriched non-expansive mappings from linear spaces to nonlinear spaces, namely, geodesic metric spaces of non-positive curvature. We prove that an enriched non-expansive mapping in complete CAT(0) space has fixed points. Moreover, we also propose simplified Mann iteration process to approximate fixed points of enriched non-expansive mappings by $\bigtriangleup$ and strong convergence in CAT(0) spaces.