A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings

被引：0

作者：

Shuang Wang ^{[1
]}

机构：

[1] Hubei Normal Univ, Dept Math, Huangshi 435002, Peoples R China

来源：

FIXED POINT THEORY AND APPLICATIONS | 2010年

基金：

美国国家科学基金会;

关键词：

Differential Geometry; Nonexpansive Mapping; Strong Convergence; Computational Biology; Full Article;

D O I：

10.1155/2010/805326

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper by Hu in 2008, the author proved a strong convergence result for nonexpansive mappings using a modified Halpern's iteration algorithm. Unfortunately, the case lim(n ->infinity) beta(n) = 1 does not guarantee the strong convergence of the sequence {x(n)}. In this note, we provide a counter-example to the theorem. Copyright (C) 2010 Shuang Wang.

引用

页数：2

共 50 条

[1] A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings
Shuang Wang
Fixed Point Theory and Applications, 2010
[2] Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings
Hu, Liang-Gen
FIXED POINT THEORY AND APPLICATIONS, 2008, 2008 (1)
[3] Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings
Liang-Gen Hu
Fixed Point Theory and Applications, 2008
[4] Strong convergence of a modified Halpern-iteration for asymptotically quasi-φ-nonexpansive mappings
Wu, Chang-Qun
Hao, Yan
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2013, 21 (01): : 261 - 276
[5] Halpern's Iteration for Nonexpansive Mappings
Lopez, Genaro
Martin-Marquez, Victoria
Xu, Hong-Kun
NONLINEAR ANALYSIS AND OPTIMIZATION I: NONLINEAR ANALYSIS, 2010, 513 : 211 - 231
[6] A STRONG CONVERGENCE THEOREM UNDER HALPERN'S ITERATION FOR RELATIVELY NONEXPANSIVE MAPPINGS IN A BANACH SPACE
Takahashi, Wataru
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2021, 22 (01) : 1 - 17
[7] A STRONG CONVERGENCE THEOREM UNDER HALPERN'S ITERATION FOR GENERALIZED NONEXPANSIVE MAPPINGS IN A BANACH SPACE
Hojo, Mayumi
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2022, 23 (02) : 377 - 395
[8] Strong Convergence of Modified Iteration Processes for Relatively Nonexpansive Mappings
Kim, Tae-Hwa
Lee, Hwa-Jung
KYUNGPOOK MATHEMATICAL JOURNAL, 2008, 48 (04): : 685 - 703
[9] Convergence of a modified Halpern-type iteration algorithm for quasi-φ-nonexpansive mappings
Qin, Xiaolong
Cho, Yeol Je
Kang, Shin Min
Zhou, Haiyun
APPLIED MATHEMATICS LETTERS, 2009, 22 (07) : 1051 - 1055
[10] Strong Convergence of Modified Iteration Processes for Relatively Weak Nonexpansive Mappings
Boonchari, Daruni
Saejung, Satit
KYUNGPOOK MATHEMATICAL JOURNAL, 2012, 52 (04): : 433 - 441

← 1 2 3 4 5 →