STRONG CONVERGENCE THEOREMS OF MODIFIED MANN ITERATIVE PROCESS FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES

被引：0

作者：

Haifang Liu ^{[1
]}

Rudong Chen ^{[1
]}

机构：

[1] Tianjin Polytech Univ, Dept Math, Tianjin 300160, Peoples R China

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2011年 / 5卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Nonexpansive mapping; strong positive operator; variational inequality; iterative algorithm; STRICT PSEUDO-CONTRACTIONS; FIXED-POINT SET; BANACH-SPACES; SEMIGROUPS; WEAK; APPROXIMATION; OPTIMIZATION; FAMILY;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this article is to modify normal Mann's iterative process to have strong convergence for nonexpansive mappings in the formework of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the fixed point of nonexpansive mappings which is the unique solution of a variational inequality, which is also the optimality condition for a minimization problem.

引用

页码：141 / 153

页数：13

共 50 条

[1] Strong convergence theorems of modified Mann iterative process for strict pseudo-contractions in Hilbert spaces
Qin, Xiaolong
Shang, Meijuan
Kang, Shin Min
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (03) : 1257 - 1264
[2] Strong Convergence Theorems of a General Iterative Process for Two Nonexpansive Mappings in Banach Spaces
Sunthrayuth, Pongsakorn
Kumam, Poom
[J]. JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2012, 14 (03) : 446 - 457
[3] Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces
Yao, Yonghong
Liou, Yeong Cheng
Marino, Giuseppe
[J]. FIXED POINT THEORY AND APPLICATIONS, 2009,
[4] WEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES
Miao, Yu
Li, Junfen
[J]. APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2008, 2 (02) : 197 - 204
[5] Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces
Yonghong Yao
Yeong Cheng Liou
Giuseppe Marino
[J]. Fixed Point Theory and Applications, 2009
[6] Weak and Strong Convergence Theorems of Quasi-Nonexpansive Mappings in a Hilbert Spaces
Gang Eun Kim
[J]. Journal of Optimization Theory and Applications, 2012, 152 : 727 - 738
[7] Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces
Takahashi, Wataru
Takeuchi, Yukio
Kubota, Rieko
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 341 (01) : 276 - 286
[8] Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces
Nakajo, K
Shimoji, K
Takahashi, W
[J]. TAIWANESE JOURNAL OF MATHEMATICS, 2006, 10 (02): : 339 - 360
[9] Weak and Strong Convergence Theorems of Quasi-Nonexpansive Mappings in a Hilbert Spaces
Kim, Gang Eun
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2012, 152 (03) : 727 - 738
[10] WEAK AND STRONG CONVERGENCE OF THE MODIFIED MANN ITERATION PROCESS FOR NONEXPANSIVE MAPPINGS
Kim, Gang Eun
[J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2012, 13 (03) : 449 - 457

← 1 2 3 4 5 →