对Ky Fan极小极大不等式的推广  

Generalization of Ky Fan's Minimax Inequality

作　　者：韩敏[1] 

机构地区：[1]北京工业大学应用数理学院,北京100022

出　　处：《北京工业大学学报》2003年第1期83-86,共4页Journal of Beijing University of Technology

摘　　要：利用凸空间以及紧闭集的性质把Ky Fan极小极大不等式推广为拓扑向量空间和拓扑空间的乘积空间上两个函数的极小极大不等式,并由此得到一个拓扑向量空间和拓扑空间的乘积空间上关于一个函数的极小极大不等式。进一步得到了一个新的截口定理,是对以前的一此截口定理的推广。通过严密的证明证实所得到的截口定理和极小极大不等式是等价的,前者是后者的几何形式。Based on the property of convex and compactly closed set, the author generalizes Ky Fan minimax inequality as new minimax inequality of two functions on the product space of a topological vector space and a topological space, and from this obtains a minimax inequality about one function on this product space. At the same time a section theorem is also obtained, which is the generalization of many former section theorems. It has been verified that the obtained section theorem and minimax inequality are equivalent, the former being the geometrical form of the latter.

关 键 词：拓扑空间 Hausdorff拓扑向量空间 极小极大不等式 截口定理 凸空间 下半连续 准凹 紧闭集 

分 类 号：O189[理学—数学]