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

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