| 自反Ballach空间中极大单调集值映射变分不等式的解的存在性 |
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| 引用本文： | 蔡时连,范江华.自反Ballach空间中极大单调集值映射变分不等式的解的存在性[J].北京建筑工程学院学报,2006,22(4):77-79. |
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| 作者姓名： | 蔡时连 范江华 |
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| 作者单位： | [1]北京建筑工程学院图书馆,北京100044 [2]广西师范大学数计学院,广西桂林541004 |
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| 摘 要： | 研究一般凸集约束下自反Banach空间极大单调集值映射变分不等式的解的存在性，首先利用集值映射锐角原理，提出了一个例外簇的概念，由此给出变分不等式问题解存在的一个充分条件．对于伪单调变分不等式问题，它是解存在的充要条件．把文献1]变分不等式问题解的存在性推广到自反Banach空间极大单调集值映射．
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| 关 键 词： | 自反Banach空间 集值映射 极大单调 例外簇 变分不等式 |
| 文章编号： | 1004-6011（2006）04-0077-03 |
| 收稿时间： | 2006-09-18 |
| 修稿时间： | 2006年9月18日 |
Existence of the Solutions of the Variational Inequality Problem with a Maximal Monotone Set-valued Map on a Reflexive Banach Space |
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| Cai Shilian, Fan Jianghua.Existence of the Solutions of the Variational Inequality Problem with a Maximal Monotone Set-valued Map on a Reflexive Banach Space[J].Journal of Beijing Institute of Civil Engineering and Architecture,2006,22(4):77-79. |
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| Authors: | Cai Shilian Fan Jianghua |
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| Affiliation: | 1 .Library, Beijing 100044; 2.Dept. of Math., Guangxi Normal Univ., Guilin Guangxi 541004 |
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| Abstract: | The existence of the solutions of the variational inequality problem with a maximal monotone set-valued map on a reflexive a Banach space under a general convex constrained set is discussed in this paper. A concept exceptional family for the problem by using acute angle principle of set-valued map is proposed. Based on this concept, a sufficient condition for the existence of the solution of the variational inequality problem is given. Also that this condition is both necessary and sufficient to pseudomonotone variational inequalities problem, is confivmed. |
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| Keywords: | reflexive Banach space set-valued map maximal monotone exceptional family variational inequality |
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