Approximating common endpoints of multivalued generalized nonexpansive mappings in hyperbolic spaces

In this paper, we introduce a new modified iteration process for approximating common endpoint of a multivalued alpha-nonexpansive mapping and a multivalued mapping satisfying condition (E') in uniformly convex hyperbolic spaces. As a by-product, we improve the main results of Panyanak (2018) with a new and faster algorithm for two multivalued mappings. Moreover, we give a numerical example to substantiate our results. Our work is new and holds simultaneously in uniformly convex Banach spaces as well as CAT(0) spaces. (c) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper introduces a new modified iteration process for approximating the common endpoint of multivalued mappings in uniformly convex hyperbolic spaces, and improves upon previous results. A numerical example is provided to support the findings, which hold in both uniformly convex Banach spaces and CAT(0) spaces.