可数族弱Bregman相对非扩展映像的收敛性分析

数学物理学报 ›› 2014, Vol. 34 ›› Issue (1): 70-79.

可数族弱Bregman相对非扩展映像的收敛性分析

陈加伟¹, 万仲平², 赵烈济³

1.西南大学数学与统计学院重庆 400715;
2.武汉大学数学与统计学院武汉 430072|
3.庆尚国立大学教育学院数学教育系韩国晋州 660-701

收稿日期:2012-04-19 修回日期:2013-08-17 出版日期:2014-02-25 发布日期:2014-02-25
基金资助:
国家自然科学基金(71171150)和中央高校基本科研业务专项基金(201120102020004)资助.

Convergence Analysis for Countable Family of Weak Bregman Relatively Nonexpansive Mappings

CHEN Jia-Wei¹, WAN Zhong-Peng², ZHAO Lie-Ji³

1.School of Mathematics and Statistics, Southwest University, Chongqing 400715;
2.School of Mathematics and Statistics, Wuhan University, Wuhan 430072;
3.Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea

Received:2012-04-19 Revised:2013-08-17 Online:2014-02-25 Published:2014-02-25
Supported by:
国家自然科学基金(71171150)和中央高校基本科研业务专项基金(201120102020004)资助.

摘要/Abstract

摘要：

在自反Banach空间中, 引入可数族弱Bregman相对非扩张映像概念, 构造了两种迭代算法求解可数族弱Bregman相对非扩张映像的公共不动点. 在适当条件下, 证明了两种迭代算法产生的序列的强收敛性.

关键词: 强收敛性定理, Bregman距离, Bregman投影, (弱)Bregman相对非扩张映像

Abstract:

A notion of countable family of weak Bregman relatively nonexpansive mappings is introduced in reflexive Banach space. We construct two iterative algorithms for finding a common fixed point of a countable family of weak Bregman relatively nonexpansive mappings in Banach spaces. Finally, the strong convergence of the proposed algorithms are also proved under appropriate conditions.

Key words: Strong convergence theorem, Bregman distance, Bregman projection, (weak) Bregman relatively nonexpansive map

中图分类号:

47H09

陈加伟, 万仲平, 赵烈济. 可数族弱Bregman相对非扩展映像的收敛性分析[J]. 数学物理学报, 2014, 34(1): 70-79.

CHEN Jia-Wei, WAN Zhong-Peng, ZHAO Lie-Ji. Convergence Analysis for Countable Family of Weak Bregman Relatively Nonexpansive Mappings[J]. Acta mathematica scientia,Series A, 2014, 34(1): 70-79.

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