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

Zhang Shi-sheng; Yang Gan-shan

Volume 11 Issue 11

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Article Navigation > Applied Mathematics and Mechanics > 1990 > 11(11): 961-968

Zhang Shi-sheng, Yang Gan-shan. Some Further Generalizations of Ky Fan’s Minimax Inequality and Its Applications to Variational Inequalities[J]. Applied Mathematics and Mechanics, 1990, 11(11): 961-968.

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

Zhang Shi-sheng¹,
Yang Gan-shan²

1.
Department of Mathematics, Sichuan University, Chengdu;
2.
Department of Mathematics, Yunnan National Institute, Kunming

Received Date: 1989-11-10
Publish Date: 1990-11-15

Abstract

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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References

[1]	Yeh,C.L.A minimax inequalities and its applications to variational inequalities,Pacific J.Math.,97(1981),477-480.
[2]	Shin,M.H.and K.K.Tan,Generalized quasi-variational inequalities in L.C.S.,J.Math.Anal Appl.,108(1985),333-343.
[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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