| 可数族弱Bregman相对非扩展映像的收敛性分析 |
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| 引用本文： | 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(A辑), 2014, 34(1): 70-79 |
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| 作者姓名： | 陈加伟 万仲平 赵烈济 |
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| 作者单位： | 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 |
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| 基金项目： | 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. |
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| 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.
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| 关 键 词： | 强收敛性定理 Bregman距离 Bregman投影 (弱)Bregman相对非扩张映像. |
| 收稿时间： | 2012-04-19 |
| 修稿时间： | 2013-08-17 |
Convergence Analysis for Countable Family of Weak BregmanRelatively Nonexpansive Mappings |
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| CHEN Jia-Wei,WAN Zhong-Peng,ZHAO Lie-Ji. Convergence Analysis for Countable Family of Weak BregmanRelatively Nonexpansive Mappings[J]. Acta Mathematica Scientia, 2014, 34(1): 70-79 |
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| Authors: | CHEN Jia-Wei WAN Zhong-Peng ZHAO Lie-Ji |
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| Affiliation: | 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 |
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| 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. |
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| Keywords: | Strong convergence theoremzz Bregman distancezz Bregman projectionzz (weak) Bregman relatively nonexpansive mapzz |
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