Fan Ky极大极小不等式的进一步推广及对变分不等式的应用

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基金项目: 国家自然科学基金资助项目

Some Further Generalizations of Ky Fan’s Minimax Inequality and Its Applications to Variational Inequalities

摘要: 本文引出广义KKM映象的概念,其包含著名的KKM映象为特例.借助于这一映象,我们给出著名的KKM定理和Fan Ky极大极小不等式以一种新的推广形式.作为应用,我们考虑了变分不等式解的存在性问题.本文结果是引文[1～6]中相应结果的改进和发展.
- 广义KKM映象 /
- 上半连续 /
- γ-对角拟凸 /
- 鞍点
Abstract: The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality.As applications, we utilize the results presented in this paper to study the saddle point problem and the existence problem of solutions for a class of quasi-variational inequalities.The results obtained in this paper extend and improve some recent results of [1-6].
- generalized KKM mapping /
- upper-semicontinuous /
- γ /
- -diagonally quasi-convex

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[3]	Zhou,J.X.and G,Chen,Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities,J.Math.Anal.Appl.,132(1988),213-223.
[4]	Bardaro,C.and R.Ceppitelli,Some further generalizations of Knaster-Kuratowaki-Mazurkiewcz theorem and minimax inequalities,J.Math.Anal.Appl.,132(1988),484-490.
[5]	Aubin,J.P.,and I.Ekeland,Applied Nonlinear Analysis,New York.Wiley-Interscience Publication(1984).
[6]	Lassonde,M.,On the use of KKM multifunctions in fixed point theory and related topics,J.Math.Anal.Appl.,97(1985),151-201.
[7]	张石生、舒永录,多值映象的变分不等式及其在非线性规划和鞍点问题的应用,应用数学学报 (待发表).

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