学术
Banach空间中两个极大单调算子公共零点的迭代格式
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魏利[1,2] 周海云[2,3]
[1]河北经贸大学数学与统计学学院,河北石家庄050061 [2]军械工程学院应用数学与力学研究所,河北石家庄050003 [3]河北师范大学数学与信息科学学院,河北石家庄050016
国际标准刊号：ISSN 1000-341X
国内统一刊号：CN 21-1208
摘 要:
令E为实光滑、一致凸Banach空间，E^＊为其对偶空间．令A，B包含E×E^＊为极大单调算子且A^-10∩B^-10≠0．本文将引入新的迭代格式，利用Lyapunov泛函与广义投影算子等技巧，证明迭代序列弱收敛于极大单调算子A和B的公共零点．[著者文摘]
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文章出处:
《数学研究与评论》-2007年27卷4期 -913-918页
Journal of Mathematical Research and Exposition
栏目信息:
分 类 号:
文献标识码:
A
文章编号:
1000-341X（2007）04-0913-06
[参考文献]
An Iterative Algorithm of Common Zero Points for Two Maximal Monotone Operators in Banach Space
WEI Li, ZHOU Hai-yun （1. School of Mathematics and Statistics, Hebei University of Economics and Business, Hebei 050016, China; 2. Institute of Applied Mathematics and Mechanics, Ordnance Engineering College, Hebei 050003, China; 3. Institute of Mathematics and Information Science, Hebei Normal University, Hebei 050016, China ）
Abstract:
Let E be a real smooth and uniformly convex Banach space with E^＊ being its duality space. Let A, B belong to E×E^＊ be maximal monotone operators with A^-10 ∩ B^-10 ≠ 0. A new iterative algorithm is introduced which is proved to be weakly convergent to common zero points of maximal monotone operators A and B by using the techniques of Lyapunov functional and generalized projection operator, etc.[著者文摘]
Key words:
Lyapunov functional; maximal monotone operator; uniformly convex Banach space.
收稿日期: 2005-10-08
修订日期: 2006-07-02
基金资助:
国家自然科学基金（10471033）.
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