Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups

被引：621

作者：

Nakajo, K ^{[1
]}

Takahashi, W ^{[1
]}

机构：

[1] Tokyo Inst Technol, Dept Math & Comp Sci, Meguro Ku, Tokyo 1528552, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2003年 / 279卷 / 02期

关键词：

nonexpansive; nonexpansive semigroup; strong convergence; metric projection; resolvent;

D O I：

10.1016/S0022-247X(02)00458-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in Hilbert spaces by the hybrid method in the mathematical programming. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：372 / 379

页数：8

共 12 条

[1] ATSUSHIBA S, NONLINEAR ANAL CONVE, P102
[2] ON THE CONVEX APPROXIMATION PROPERTY AND THE ASYMPTOTIC-BEHAVIOR OF NON-LINEAR CONTRACTIONS IN BANACH-SPACES
BRUCK, RE
[J]. ISRAEL JOURNAL OF MATHEMATICS, 1981, 38 (04) : 304 - 314
[3] FIXED POINTS OF NONEXPANDING MAPS
HALPERN, B
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (06) : 957 - &
[4] Approximating solutions of maximal monotone operators in Hilbert spaces
Kamimura, S
Takahashi, W
[J]. JOURNAL OF APPROXIMATION THEORY, 2000, 106 (02) : 226 - 240
[5] MARTINET R, 1970, RIRO, V4, P154
[6] WEAK CONVERGENCE OF SEQUENCE OF SUCCESSIVE APPROXIMATIONS FOR NONEXPANSIVE MAPPINGS
OPIAL, Z
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (04) : 591 - &
[7] MONOTONE OPERATORS AND PROXIMAL POINT ALGORITHM
ROCKAFELLAR, RT
[J]. SIAM JOURNAL ON CONTROL, 1976, 14 (05): : 877 - 898
[8] Strong convergence to common fixed points of families of nonexpansive mappings
Shimizu, T
Takahashi, W
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 211 (01) : 71 - 83
[9] Shioji N., 1999, MATH JPN, V50, P57
[10] Forcing strong convergence of proximal point iterations in a Hilbert space
Solodov, MV
Svaiter, BF
[J]. MATHEMATICAL PROGRAMMING, 2000, 87 (01) : 189 - 202

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