广义变分不等式与极大极小定理
Generalized Variational Inequalities and Minimax Theorems
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摘要: 本文讨论映Hausdorff拓扑线性空间到Riesz空间[6]的算子变分问题.给出半序空间上变分不等式的绝对形式和相对形式.Abstract: In the present paper we discuss the variational problem of operator which may a Hausdorff topological linear space into a Riesz space[6] We give absolute inequality and elative inequality respectively.
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Key words:
- finite closed set /
- KKM mapping /
- Ries space /
- Gwinner theorem
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[1] Aubin,J.P.and L.Ekeland,Applied Nonlinear Analysis.New York,Wiley-Interscience Publication(1984). [2] Lassonde,M.On the use of KKM multifunctions in fixed point theorems and scalated topic J.Math.Anal.Appl.,9(1983),151-201. [3] 史榭中,完备向量格的凸集分离定理及应用,数学年刊,6A(4)(1985), 431-438, [4] 王苏生,半序线性空间的凸锥分离定理及其应用,应用数学学报,9(3)(1986),309-318. [5] Barduro,C.,and P.ceppitelli.Some further generalizations of Kanster-Kuratowski-Mazurkiewicz theorem and minimax inequalities,J.Math.Anal.Appl.,132(1988) 484-490. [6] 关肇直,《泛函分析讲义》。高等教育出版社,北京(1958). [7] Gwinner,J.On fixed points and variational inequalities-A circular tour.Nonlinear Anal.,5,5(1981),565-583.
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