Necessary and Sufficient Condition of Strong Convergence of an Implicit Iteration
Process for a Finite Family of Nonexpansive Mappings

Journal of Chongqing Jiaotong University(Natural Science) ›› 2007, Vol. 26 ›› Issue (5): 164-166.

Necessary and Sufficient Condition of Strong Convergence of an Implicit Iteration Process for a Finite Family of Nonexpansive Mappings

TANG Jing-tong

Elementary Education Colege，Chongqing Normal University，Chongqing 400700，China

Received:2006-04-17 Revised:2006-06-19 Online:2007-10-15 Published:2015-01-22

有限族渐近非扩张映象隐迭代序列收敛性充要条件

唐净熔

重庆师范大学初等教育学院，重庆 400700

作者简介:唐净熔(1957—)，女，重庆市人，副教授，主要从事非线性泛函分析研究.

Abstract

Abstract: A new two—step interative alogorithms is put forward in a uniformly convex Banach space．The necessary and sufficient condition of strong convergence of the implicit iteration process for a finite family of nonexpansive mappings is proved． The results may extend and improve some recent corresponding results．

Key words: uniformly convex Banach space, implicit iteration process, nonexpansive mappings

摘要： 在一致凸Banach空间中，提出了一类新的两步隐迭代序列，证明了此序列收敛到有限族渐近非扩张映象的公共不动点的充要条件．所得结果推广和改进了近期相应结果

关键词: 一致凸Banach空间, 隐迭代序列, 非扩张映象

CLC Number:

O177.91

TANG Jing-tong. Necessary and Sufficient Condition of Strong Convergence of an Implicit Iteration Process for a Finite Family of Nonexpansive Mappings[J]. Journal of Chongqing Jiaotong University(Natural Science), 2007, 26(5): 164-166.

唐净熔. 有限族渐近非扩张映象隐迭代序列收敛性充要条件[J]. 重庆交通大学学报（自然科学版）, 2007, 26(5): 164-166.

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[2]	LIAO Zheng-qi;HE Qing-bi. Convergence of Multistep Iterative Sequence for Asymptotically Quasi-nonexpansive Mappings of Set-value [J]. Journal of Chongqing Jiaotong University(Natural Science), 2007, 26(2): 164-166.
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