没有线性结构的极大极小定理与鞍点定理

Minimax Theorem and Saddle Point Theorem without Linear Structure

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ＦａｎＫｙ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，并把著名的鞍点定理推广到没有线性结构的拓扑空间上·

In the paper, a new kind of concavity of a function defined on a set without linear structure is introduced and a generalization of Fan Ky inequality 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.