A new three-step fixed point iteration scheme for asymptotically nonexpansive mappings

被引：13
|
作者：
Nsrakoo, Weerayuth [1 ]
Saejung, Satit [1 ]
机构：
[1] Khon Kaen Univ, Dept Math, Khon Kaen 40002, Thailand
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 181卷 / 02期
关键词：
asymptotically nonexpansive mapping; uniformly convex Banach space; Mann-type iteration; Ishikawa-type iteration; three-step iteration;
D O I：
10.1016/j.amc.2006.01.063
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the present paper, we define and study a new three-step iterative scheme inspired by Suantai [J. Math. Anal. Appl. 311 (2005) 506-517]. This scheme includes many well-known iterations, for examples, modified Mann-type, modified Ishikawa-type iterative schemes, and the three-step iterative scheme of Xu and Noor. Several convergence theorems of this scheme are established for asymptotically nonexpansive mappings. Our results extend and improve the recent ones announced by Schu [J. Math. Anal. Appl. 158 (1991) 407-413; Bull. Aust. Math. Soc. 43 (1991) 153-159], Xu and Noor [J. Math. Anal. Appl. 267 (2002) 444-453], Suantai [J. Math. Anal. Appl. 311 (2005) 506-517], and many others. A misleading conclusion of Theorem 2.6 in Suantai's paper is also corrected. (c) 2006 Elsevier Inc. All rights reserved.
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页码：1026 / 1034
页数：9
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