Generalized Krasnoselskii-Mann-Type Iteration for Nonexpansive Mappings in Banach Spaces  

作　　者：You-Cai Zhang Ke Guo Tao Wang 

机构地区：[1]School of Mathematics and Information,China West Normal University,Nanchong 637002,Sichuan,China

出　　处：《Journal of the Operations Research Society of China》2021年第1期195-206,共12页中国运筹学会会刊（英文）

基　　金：supported by the Students Innovation and Entrepreneurship Training Program Foundation of China West Normal University(No.201810638047);supported by the National Natural Science Foundation of China(Nos.11571178 and 11801455);Fundamental Research Funds of China West Normal University(Nos.17E084 and 18B031).

摘　　要：The Krasnoselskii-Mann iteration plays an important role in the approximation of fixed points of nonexpansive mappings,and it is well known that the clas-sic Krasnoselskii-Mann iteration is weakly convergent in Hilbert spaces.The weak convergence is also known even in Banach spaces.Recently,Kanzow and Shehu pro-posed a generalized Krasnoselskii-Mann-type iteration for nonexpansive mappings and established its convergence in Hilbert spaces.In this paper,we show that the generalized Krasnoselskii-Mann-type iteration proposed by Kanzow and Shehu also converges in Banach spaces.As applications,we proved the weak convergence of generalized proximal point algorithm in the uniformly convex Banach spaces.

关 键 词：Krasnoselskii-Mann-type iteration Nonexpansive mappings Weak convergence Accretive operator proximal pointalgorithm Banach spaces 

分 类 号：O17[理学—数学]