Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces

• Main Authors: Suthep Suantai, Withun Phuengrattana
• Format: Journal
• Published: 2018
• Subjects: Agricultural and Biological Sciences
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85014474299&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/47004
• Institution: Chiang Mai University

© 2017, Springer International Publishing. In this paper, we propose a new proximal point algorithm for finding a common element of the set of fixed points of nonexpansive single-valued mappings, the set of fixed points of nonexpansive multi-valued mappings, and the set of minimizers of convex and lower semi-continuous functions. We obtain Δ -convergence and strong convergence of the proposed algorithm to a common element of the three sets in CAT(0) spaces. Furthermore, we apply our convergence results to obtain in a special space of CAT(0) spaces, so-called R-tree, under the gate condition. A numerical example to support our main results is also given.