On solving the minimization problem and the fixed-point problem for nonexpansive mappings in CAT(0) spaces

Abstract

© 2016 Informa UK Limited, trading as Taylor & Francis Group. We propose a new modified proximal point algorithm combined with Halpern's iteration process for nonexpansive mappings in the framework of CAT(0) spaces. We establish a strong convergence theorem under some mild conditions. Our results extend some known results which appeared in the literature.