平衡问题和不动点问题的公共元的混杂算法

数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 720-728.

平衡问题和不动点问题的公共元的混杂算法

高兴慧¹, 周海云², 高改良²

1.延安大学数学与计算机科学学院陕西延安 716000|2.石家庄军械工程学院数学系石家庄 050003

收稿日期:2009-11-17 修回日期:2010-10-20 出版日期:2011-06-25 发布日期:2011-06-25
基金资助:
国家自然科学基金(10771050)和陕西省教育厅科研计划项目（11JK0486)资助

Hybrid Algorithms of Common Elements for Equilibrium Problems and Fixed Point Problems

GAO Xing-Hui¹, ZHOU Hai-Yun², GAO Gai-Liang²

1.College of Mathematics and Computer Science, Yan'an University, Shaanxi Yan'an 716000|2.Department of Mathematics, Shijiazhuang Mechanical Engineering College, |Shijiazhuang 050003

Received:2009-11-17 Revised:2010-10-20 Online:2011-06-25 Published:2011-06-25
Supported by:
国家自然科学基金(10771050)和陕西省教育厅科研计划项目（11JK0486)资助

摘要/Abstract

摘要：

In strictly convex and uniformly smooth Banach spaces with the K-K property,
a new hybrid projection method is proposed to approximate common elements for the set
of common fixed points of two quasi-$\phi$-nonexpansive mappings
and the set of solutions of an equilibrium problem. A strong convergence theorem of the common elements
is proved by using generalized projection operator, the K-K property and
other analysis techniques. The results of this paper improve and extend recent
some relative results.在严格凸的具有K-K性质的一致光滑Banach空间中, 设计了一种新混杂算法用以逼近两个Φ -非扩张映像的公共不动点集和一个平衡问题解集的公共元素, 并利用广义投影算子和K-K性质等技巧证明了该算法的强收敛性. 所得结果是近期相关结果的改进与推广.

关键词: 混杂算法, 平衡问题, 拟Φ -非扩张映像

Abstract:

Key words: Hybrid algorithms, Equilibrium problem, Quasi-Φ-nonexpansive mapping.

中图分类号:

47H05

高兴慧, 周海云, 高改良. 平衡问题和不动点问题的公共元的混杂算法[J]. 数学物理学报, 2011, 31(3): 720-728.

GAO Xing-Hui, ZHOU Hai-Yun, GAO Gai-Liang. Hybrid Algorithms of Common Elements for Equilibrium Problems and Fixed Point Problems[J]. Acta mathematica scientia,Series A, 2011, 31(3): 720-728.

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