拓扑向量空间中的广义向量F-隐补问题

数学物理学报 ›› 2010, Vol. 30 ›› Issue (6): 1528-1533.

拓扑向量空间中的广义向量F-隐补问题

冯世强|高大鹏|李军

西华师范大学数学与信息学院四川南充 637002

收稿日期:2008-07-12 修回日期:2009-12-22 出版日期:2010-12-25 发布日期:2010-12-25
基金资助:
国家自然科学基金(60804065)、四川省教育厅重点项目(07ZA123)和西华师范大学科研启动基金(08B075)资助

Generalized Vector F-implicit Complementarity Problems in Topological Vector Spaces

FENG Shi-Qiang, GAO Da-Feng, LI Jun

School of Mathematics and Information, China West Normal University, Sichuan Nanchong |637002

Received:2008-07-12 Revised:2009-12-22 Online:2010-12-25 Published:2010-12-25
Supported by:
国家自然科学基金(60804065)、四川省教育厅重点项目(07ZA123)和西华师范大学科研启动基金(08B075)资助

摘要/Abstract

摘要：

该文在拓扑向量空间中引入了一类新的向量F-隐补问题(简记为:(GVF-ICP))和两类(强和弱)向量F-隐变分不等式问题(分别简记为:(GVF-IVI)₁和(GVF-IVI)₂). 在齐性条件下得到了(GVF-ICP)与(GVF-IVI)₁的等价关系, 同时在适当假设下利用KKM定理得到了(GVF-IVI)₂的新的解的存在性定理.

关键词: 广义向量F-隐补问题, 广义向量F-隐变分不等式, 拓扑向量空间, KKM定理, 存在性

Abstract:

In this work, the authors introduce a new class of vector F-implicit complementarity problems (for short, GVF-ICP) and two classes of
(strong and weak) vector F-implicit variational inequalities (for short, (GVF-IVI)₁ and (GVF-IVI)₂, respectively) in topological vector spaces. They present the equivalence between (GVF-ICP) and (GVF-IVI)₁ under homogeneity. They also derive some new existence theorems of solutions for (GVF-IVI)₂by using the KKM theorem under some suitable assumptions.

Key words: Generalized vector F-implicit complementarity problem, Generalized vector F-implicit variational inequality, Topological vector space, KKM theorem, Exsitence

中图分类号:

90J33

冯世强, 高大鹏, 李军. 拓扑向量空间中的广义向量F-隐补问题[J]. 数学物理学报, 2010, 30(6): 1528-1533.

FENG Shi-Qiang, GAO Da-Feng, LI Jun. Generalized Vector F-implicit Complementarity Problems in Topological Vector Spaces[J]. Acta mathematica scientia,Series A, 2010, 30(6): 1528-1533.

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