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论文摘要

可数族Bregman全局拟-渐进非扩张映射的均衡问题和强收敛定理

Strong convergence theorems for equilibrium problem and countable Bregman totally quasi-asymptotically nonexpansive mappings

作者:沈金良(福州大学至诚学院);朱胜(福建农林大学金山学院);黄建华(福州大学数学与计算机科学学院)

Author:shen jinliang();zhu sheng(Jinshan College of Fujian Agriculture and Forestry University);huang jianhua(Institute of Mathematics and Computer, Fuzhou University)

收稿日期:2016-07-09          年卷(期)页码:2017,54(2):261-267

期刊名称:四川大学学报: 自然科学版

Journal Name:Journal of Sichuan University (Natural Science Edition)

关键字:均衡问题;Bregman全局拟-渐进非扩张映射;Bregman距离;自反Banach空间

Key words:equilibrium problem; Bregman totallyquasi-asymptotically nonexpansive mapping; Bregman distance; reflexive Banach space.

基金项目:福建省自然科学基金资助项目(2014J01008 ),福建省中青年教师教育科研项目(JA15624)

中文摘要

在实自反的Banach空间中,针对可数族Bregman全局拟-渐进非扩张映射的公共不动点和均衡问题的公共解,构造了一类新型的混合迭代算法,在适当条件下证明了该算法产生的序列的强收敛性.更进一步地,将此方法应用到求解极大单调算子的零点问题上.

英文摘要

In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of countable Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.

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