广义凸空间上截口定理及其对变分不等式的应用

数学物理学报 ›› 2011, Vol. 31 ›› Issue (4): 1036-1044.

广义凸空间上截口定理及其对变分不等式的应用

朴勇杰

延边大学理学院数学系吉林延吉 133002

收稿日期:2009-10-08 修回日期:2010-11-06 出版日期:2011-08-25 发布日期:2011-08-25
基金资助:
吉林省教育厅自然科学基金(2011[434])资助

Section Theorems and Their Applications to Variational Inequalities on Generalized Convex Spaces

PIAO Yong-Jie

Department of Mathematics, College of Science, Yanbian University, Jilin Yanji 133002

Received:2009-10-08 Revised:2010-11-06 Online:2011-08-25 Published:2011-08-25
Supported by:
吉林省教育厅自然科学基金(2011[434])资助

摘要/Abstract

摘要：

该文得到了广义凸空间上的KKM型定理并由此得到了截口问题的解析型择一性定理. 作为上述结论的应用, 讨论了广义凸空间上变分不等式
解的存在性问题. 该文的主要结论改进和推广了文献中的相应结论.

关键词: 广义凸空间, &Gamma, -凸子集, &Gamma, -凸函数, 上[下]半连续, KKM映射, 转移闭值

Abstract:

The KKM type theorem on generalized convex spaces is introduced, and from which, an analytic alternative type theorem of section problem is obtained. As applications of the above results, the existence problems of solution for variational inequalities on generalized convex spaces are discussed. The main results of this paper improve and generalize the corresponding results in recent literatures.

Key words: Generalized convex space, Γ-convex subset, Γ-convex function, Upper[resp. lower] semicontinuous, KKM map, Transfer closed valued

中图分类号:

47H02

朴勇杰. 广义凸空间上截口定理及其对变分不等式的应用[J]. 数学物理学报, 2011, 31(4): 1036-1044.

PIAO Yong-Jie. Section Theorems and Their Applications to Variational Inequalities on Generalized Convex Spaces[J]. Acta mathematica scientia,Series A, 2011, 31(4): 1036-1044.

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