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

作     者：Suantai, Suthep Phuengrattana, Withun 

作者机构：Chiang Mai Univ Fac Sci Dept Math Chiang Mai 50200 Thailand Nakhon Pathom Rajabhat Univ Fac Sci & Technol Dept Math Mueang Nakhon Pathom 730000 Nakhon Pathom Thailand 

出 版 物：《MEDITERRANEAN JOURNAL OF MATHEMATICS》 (地中海数学杂志)

年 卷 期：2017年第14卷第2期

页      面：1-17页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Thailand Research Fund [RTA5780007] 

主　　题：Geodesic metric spaces fixed point proximal point algorithm nonexpansive mappings 

摘      要：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 multivalued mappings, and the set of minimizers of convex and lower semicontinuous functions. We obtain Delta-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.