有限簇非扩张映象的不动点定理及逼近算法

数学物理学报 ›› 2012, Vol. 32 ›› Issue (3): 540-546.

有限簇非扩张映象的不动点定理及逼近算法

闻道君¹|邓磊²

1.重庆工商大学数学与统计学院重庆 400067；2.西南大学数学与统计学院重庆 400715

收稿日期:2010-09-27 修回日期:2011-10-18 出版日期:2012-06-25 发布日期:2012-06-25
基金资助:
国家自然科学基金(11001287)、重庆市自然科学基金(CSTC 2010BB9254)和重庆市教委科技研究项目(KJ 110701)资助

Approximate Methods and Theorems of Common Fixed-points for a Finite Family of Nonexpansive Mappings

WEN Dao-Jun¹, DENG Lei²

1.College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067；2.School of Mathematics and Statistics, Southwest University, Chongqing |400715

Received:2010-09-27 Revised:2011-10-18 Online:2012-06-25 Published:2012-06-25
Supported by:
国家自然科学基金(11001287)、重庆市自然科学基金(CSTC 2010BB9254)和重庆市教委科技研究项目(KJ 110701)资助

摘要/Abstract

摘要：

在具有一致Gâteaux可微范数的Banach空间中, 研究了一个逼近有限簇非扩张映象不动点的修正的Mann 迭代, 并在一定条件下证明了该迭代格式所产生的序列强收敛到有限簇非扩张映象的某个公共不动点.

关键词: 非扩张映象, 公共不动点, 修正的Mann迭代, Banach极限

Abstract:

In this paper, a modified Mann iteration is proposed for finding a common fixed-point of a finite family of nonexpansive mappings, in which strong convergence theorems are proved under some suitable conditions. The results presented in this paper can be considered as an extension and improvement of some previously known results.

Key words: Nonexpansive mappings, Common fixed-point, Modified Mann iteration, Banach limits

中图分类号:

47H05

闻道君, 邓磊. 有限簇非扩张映象的不动点定理及逼近算法[J]. 数学物理学报, 2012, 32(3): 540-546.

WEN Dao-Jun, DENG Lei. Approximate Methods and Theorems of Common Fixed-points for a Finite Family of Nonexpansive Mappings[J]. Acta mathematica scientia,Series A, 2012, 32(3): 540-546.

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