Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces

被引：165

作者：

Xu, BL

Noor, MA

机构：

[1] Oufu Normal Univ, Dept Math, Shandong 273165, Peoples R China

[2] Etisalat Coll Engn, Sharjah, U Arab Emirates

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2002年 / 267卷 / 02期

关键词：

three-step iterations; asymptotically nonexpansive mappings; uniformly convex Banach spaces; Mann-type and Ishikawa-type iterations;

D O I：

10.1006/jmaa.2001.7649

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results. (C) 2002 Elsevier Science (USA).

引用

页码：444 / 453

页数：10

共 22 条

[1] WEAK CONVERGENCE TO FIXED-POINT OF AN ASYMPTOTICALLY NONEXPANSIVE MAP
BOSE, SC
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 68 (03) : 305 - 308
[2] CHANG SS, WEAK CONVERGENCE FIX
[3] Fixed point iteration for pseudocontractive maps
Chidume, CE
Moore, C
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (04) : 1163 - 1170
[4] GLOWINSKI R, 1989, AUGEMENTED LAGRANGIA
[5] FIXED-POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS
GOEBEL, K
KIRK, WA
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 35 (01) : 171 - &
[6] Convergence analysis and applications of the Glowinski-Le Tallec splitting method for finding a zero of the sum of two maximal monotone operators
Haubruge, S
Nguyen, VH
Strodiot, JJ
[J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1998, 97 (03) : 645 - 673
[7] MANN ITERATION PROCESS IN HILBERT-SPACE
HICKS, TL
KUBICEK, JD
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1977, 59 (03) : 498 - 504
[8] FIXED-POINTS BY A NEW ITERATION METHOD
ISHIKAWA, S
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 44 (01) : 147 - 150
[9] Liu QH, 1996, NONLINEAR ANAL-THEOR, V26, P1835
[10] MEAN VALUE METHODS IN ITERATION
MANN, WR
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 4 (03) : 506 - 510

← 1 2 3 →