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

被引：0
作者：
You-Cai Zhang
Ke Guo
Tao Wang
机构：
[1] China West Normal University,School of Mathematics and Information
来源：
Journal of the Operations Research Society of China | 2021年 / 9卷
关键词：
Krasnoselskii–Mann-type iteration; Nonexpansive mappings; Weak convergence; Accretive operator; proximal point algorithm; Banach spaces; 47H05; 47H09;
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学科分类号：
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 classic Krasnoselskii–Mann iteration is weakly convergent in Hilbert spaces. The weak convergence is also known even in Banach spaces. Recently, Kanzow and Shehu proposed 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.
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页码：195 / 206
页数：11
相关论文
共 34 条
  • [1] Browder FE(1965)Nonexpansive nonlinear operators in a Banach space Proc. Natl. Acad. Sci. USA 54 1041-1044
  • [2] Kirk WA(1965)A fixed point theorem for mappings which do not increase distances Am. Math. Mon. 72 1004-1006
  • [3] Krasnoselskii MA(1955)Two remarks on the method of successive approximations Uspekhi Mat. Nauk. 10 123-127
  • [4] Mann WR(1953)Mean value methods in iteration Proc. Am. Math. Soc. 4 506-510
  • [5] Reich S(1979)Weak convergence theorems for nonexpansive mappings in Banach spaces J. Math. Anal. Appl. 67 274-276
  • [6] Kirk WA(1982)Krasnoselskii’s iteration process in hyperbolic space Numer. Funct. Anal. Optim. 4 371-381
  • [7] Reich S(2000)Convergence of Krasnoselskii–Mann iterations of nonexpansive operators Math. Comput. Model. 32 1423-1431
  • [8] Zaslavski AJ(2004)Solving monotone inclusions via compositions of nonexpansive averaged operators Optimization 53 475-504
  • [9] Combettes PL(2016)Convergence of inexact Mann iterations generated by nearly nonexpansive sequences and applications Numer. Funct. Anal. Optim. 37 1312-1338
  • [10] Sahu DR(2007)Robustness of Mann’s algorithm for nonexpansive mappings J. Math. Anal. Appl. 327 1105-1115
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