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

被引：312
|
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
收藏
页码：276 / 286
页数：11
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