Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces

被引：319

作者：

Takahashi, Wataru ^{[1
]}

Takeuchi, Yukio ^{[1
]}

Kubota, Rieko ^{[2
]}

机构：

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

[2] Yokohama Natl Univ, Grad Sch Engn, Div Phys Elect & Comp Engn, Yokohama, Kanagawa 2408501, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 341卷 / 01期

关键词：

nonexpansive mapping; fixed point; maximal monotone operator; one-parameter nonexpansive semigroup; hybrid method;

D O I：

10.1016/j.jmaa.2007.09.062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes Nakajo and Takahashi's theorems [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], simultaneously. Furthermore, we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from Nakajo and Takahashi. Using this theorem, we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a Hilbert space. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：276 / 286

页数：11

共 16 条

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[2]

BREZIS H, 1973, MATH STUDIES, V6, P5

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