Convergence of a general iterative method for nonexpansive mappings in Hilbert spaces

被引：23

作者：

Cho, Yeol Je ^{[2
,3
]}

Qin, Xiaolong ^{[1
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math, Chinju 660701, South Korea

[2] Gyeongsang Natl Univ, Dept Math Educ, Chinju 660701, South Korea

[3] Gyeongsang Natl Univ, RINS, Chinju 660701, South Korea

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 228卷 / 01期

关键词：

Nonexpansive mapping; Strong convergence; Fixed point; Hilbert space; Modified Ishikawa iterative process; FIXED-POINTS; BANACH-SPACES; THEOREMS; APPROXIMATION; SEMIGROUPS;

D O I：

10.1016/j.cam.2008.10.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. The results improve and extend the corresponding results of many others. (c) 2008 Elsevier B.V. All rights reserved.

引用

页码：458 / 465

页数：8

共 20 条

[1]

Deutsch F, 1998, NUMER FUNC ANAL OPT, V19, P33, DOI 10.1080/01630569808816813

[2] EXAMPLE CONCERNING FIXED-POINTS [J].

GENEL, A ;

LINDENSTRAUSS, J .

ISRAEL JOURNAL OF MATHEMATICS, 1975, 22 (01) :81-92

[3] FIXED-POINTS BY A NEW ITERATION METHOD [J].

ISHIKAWA, S .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 44 (01) :147-150

[4] Strong convergence of modified Mann iterations [J].

Kim, TH ;

Xu, HK .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 61 (1-2) :51-60

[5] MEAN VALUE METHODS IN ITERATION [J].

MANN, WR .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 4 (03) :506-510

[6] A general iterative method for nonexpansive mappings in Hilbert spaces [J].

Marino, G ;

Xu, HK .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 318 (01) :43-52

[7] Viscosity approximation methods for fixed-points problems [J].

Moudafi, A .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 241 (01) :46-55

[8] Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups [J].

Nakajo, K ;

Takahashi, W .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 279 (02) :372-379

[9] Strong convergence of the composite Halpern iteration [J].

Qin, Xiaolong ;

Su, Yongfu ;

Shang, Meijuan .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 339 (02) :996-1002

[10] Approximation of a zero point of accretive operator in Banach spaces [J].

Qin, Xiaolong ;

Su, Yongfu .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 329 (01) :415-424

← 1 2 →