有限簇伪压缩映象和单调映象广义迭代法的强收敛性

数学物理学报 ›› 2014, Vol. 34 ›› Issue (5): 1123-1132.

有限簇伪压缩映象和单调映象广义迭代法的强收敛性

闻道君

重庆工商大学数学与统计学院重庆 400067

收稿日期:2013-04-28 修回日期:2014-03-01 出版日期:2014-10-25 发布日期:2014-10-25
基金资助:
国家自然科学基金(11001287, 11271388)、重庆市自然科学基金(CSTC2012jjA00039)和重庆市教委科技研究项目(KJ130712)资助.

Strong Convergence of an General Iterative Method for a Finite Family of Pseudo-Contractive and Monotone Mappings

WEN Dao-Jun

College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067

Received:2013-04-28 Revised:2014-03-01 Online:2014-10-25 Published:2014-10-25
Supported by:
国家自然科学基金(11001287, 11271388)、重庆市自然科学基金(CSTC2012jjA00039)和重庆市教委科技研究项目(KJ130712)资助.

摘要/Abstract

摘要：

在Hilbert空间中, 建立了一个关于有限簇伪压缩映象和单调映象的广义迭代方法, 并在更弱的条件下证明了该方法所产生的序列强收敛到连续伪压缩映象不动点集和变分不等式解集的某个公共元.

关键词: 伪压缩映象, 单调映象, 不动点, 强正算子, 变分不等式

Abstract:

In Hilbert space, a general approximation method is proposed for finding a common element of the set of fixed points of a finite family of continuous pseudo-contractive mappings and solutions of variational inequalities for monotone mappings. Strong convergence of iterative sequences generated by the method are obtained under some more general conditions.

Key words: Pseudo-contractive mapping, Monotone mapping, Fixed point, Strongly positive operator, Variational inequality

中图分类号:

47H05

闻道君. 有限簇伪压缩映象和单调映象广义迭代法的强收敛性[J]. 数学物理学报, 2014, 34(5): 1123-1132.

WEN Dao-Jun. Strong Convergence of an General Iterative Method for a Finite Family of Pseudo-Contractive and Monotone Mappings[J]. Acta mathematica scientia,Series A, 2014, 34(5): 1123-1132.

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