Weak and strong convergence of splitting algorithms in Banach spaces

被引：71

作者：

Qin, Xiaolong ^{[1
,2
]}

Cho, Sun Young ^{[3
]}

Yao, Jen-Chih ^{[2
]}

机构：

[1] Hangzhou Normal Univ, Dept Math, Hangzhou, Zhejiang, Peoples R China

[2] Zhejiang Normal Univ, Dept Math, Jinhua, Zhejiang, Peoples R China

[3] China Med Univ, China Med Univ Hosp, Res Ctr Interneural Comp, Taichung, Taiwan

来源：

OPTIMIZATION | 2020年 / 69卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Accretive operator; variational inequality; nonexpansive mapping; resolvent; zero point; VISCOSITY APPROXIMATION METHODS; ACCRETIVE-OPERATORS; NONLINEAR MAPPINGS; FIXED-POINTS; NONEXPANSIVE-MAPPINGS; INCLUSION PROBLEMS; FINITE FAMILY; THEOREMS; CONTRACTIONS; ZEROS;

D O I：

10.1080/02331934.2019.1654475

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Accretive and nonexpansive operators are investigated based on two iterative algorithms. Strong and weak convergence theorems of common solutions are established in the framework of uniformly convex and q-uniformly smooth Banach spaces.

引用

页码：243 / 267

页数：25

共 50 条

[1] Weak Convergence of Greedy Algorithms in Banach Spaces
S. J. Dilworth
Denka Kutzarova
Karen L. Shuman
V. N. Temlyakov
P. Wojtaszczyk
[J]. Journal of Fourier Analysis and Applications, 2008, 14 : 609 - 628
[2] Weak Convergence of Greedy Algorithms in Banach Spaces
Dilworth, S. J.
Kutzarova, Denka
Shuman, Karen L.
Temlyakov, V. N.
Wojtaszczyk, P.
[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2008, 14 (5-6) : 609 - 628
[3] Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces
Sachiko Atsushiba
Wataru Takahashi
[J]. Fixed Point Theory and Applications, 2005
[4] Weak and strong convergence theorems for nonexpansive mappings in Banach spaces
Suzuki, T
Takahashi, W
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (04) : 2805 - 2815
[5] Weak and strong convergence theorems for nonexpansive mappings in Banach spaces
Zhao, Jing
He, Songnian
Su, Yongfu
[J]. FIXED POINT THEORY AND APPLICATIONS, 2008, 2008 (1)
[6] Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces
Atsushiba, Sachiko
Takahashi, Wataru
[J]. FIXED POINT THEORY AND APPLICATIONS, 2005, 2005 (03) : 343 - 354
[7] Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces
Jing Zhao
Songnian He
Yongfu Su
[J]. Fixed Point Theory and Applications, 2008
[8] Strong Convergence of Iterative Algorithms for Variational Inequalities in Banach Spaces
Ceng, L. C.
Schaible, S.
Yao, J. C.
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2009, 141 (02) : 265 - 283
[9] WEAK AND STRONG CONVERGENCE RESULTS OF FORWARD-BACKWARD SPLITTING METHODS FOR SOLVING INCLUSION PROBLEMS IN BANACH SPACES
Luo, Yinglin
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2020, 21 (02) : 341 - 353
[10] WEAK AND STRONG CONVERGENCE FOR QUASI-NONEXPANSIVE MAPPINGS IN BANACH SPACES
Kim, Gang Eun
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 49 (04) : 799 - 813

← 1 2 3 4 5 →