没有线性结构的极大极小定理与鞍点定理<sup>*</sup>

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没有线性结构的极大极小定理与鞍点定理^*

基金项目: * 云南省应用基础研究基金

1.
Department of Mathematics, Yunnan University, Kunming 650091, P.R.China;
2.
Institute of Educational Science, South China Normal University, Guangzhou 510631, P.R.China

摘要: 在没有线性结构的一般集合上引入了函数的一种“凹(凸)”性概念,得到一个没有线性结构的Fan Ky不等式；在此基础上,在一般的拓扑空间上建立了极大极小定理,并把着名的鞍点定理推广到没有线性结构的拓扑空间上。
- 极大极小定理 /
- 鞍点定理 /
- 拓扑空间
Abstract: In the paper,a new kind of concavity of a function defined on a set without linear structure is introduced and a generalzation of Fan Ky ineqality is given.Minimax theorem in a general topological space is obtained.Moreover,a saddle point theorem on a topological space without any linear structure is established.
- minimax theorem /
- saddle point theorem /
- topological space

[1]	J.X.Zhou and G.Chen,Diagonal convexity conditions for problems in convex analysis and guasi-variational inequalities,J.Math.Anal.Appl.,132(1) (1988),213-225.
[2]	S.S.Chang and Y.Zhang,Generalized KKM theorem and variational inequalities,J.Ma th.An al.Appl.,159(1) (1991),208-223.
[3]	张石生,《变分不等式和相补问题》,上海科学技术出版社(1991),100-159.
[4]	K.Fan,Minimax theorems,Proc.Nat.Acad.Sci.U.S.A.,39(1) (1953),42-47.
[5]	J.Gwinner and W.Oettli,Theorems of the alternative and duality for inf-sup problems,Math.Oper.Res.,19(1) (1994),238-256.
[6]	F.Terkesen,Some minimax theorems,Math.Scand,31(2) (1972),405-413.
[7]	A.Irle,A general minimax theorem,Z.Oper.Res.,29(7) (1985),229-247.
[8]	M.A.Geraghty and B.L.Lin,Topological minimax theorems,Proc.Amer.Math.Soc.,91(3) (1984),377-380.
[9]	S.S.Chang,S.W.Wu and S.W.Xiang,Atopological KKM theorem and minimax theorems,J.Math.Anal.Appl.,182(3) (1994),756-767.