On Fixed Points of Enriched Contractions and Enriched Nonexpansive Mappings

Abstract

We apply the concept of quasilinearization to introduce some enriched classes of Banach contraction mappings and analyse the fixed points of such mappings in the setting of Hadamard spaces. We establish existence and uniqueness of the fixed point of such mappings. To approximate the fixed points, we use an appropriate Krasnoselskij-type scheme for which we establish $\Delta$ and strong convergence theorems. Furthermore, we discuss the fixed points of local enriched contractions and Maia-type enriched contractions in Hadamard spaces setting. In addition, we establish demiclosedness-type property of enriched nonexpansive mappings. Finally, we present some special cases and corresponding fixed point theorems.