拓扑空间中的广义KKM型定理及其应用  

Generalized KKM-type theorems and their applications in topological space

作　　者：叶明武[1] 彭定涛[1] 

机构地区：[1]贵州大学理学院,贵州贵阳550025

出　　处：《安徽大学学报（自然科学版）》2012年第5期16-19,共4页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11171018);贵州省科学技术基金资助项目(20102133)

摘　　要：介绍线性拓扑空间上的KKM定理,在无任何线性结构的拓扑空间中建立了基于弱广义KKM映射的广义KKM型定理,并且应用新的广义KKM型定理得到非紧拓扑空间上的一些鞍点定理及Nash平衡存在性定理.论文的结果统一和改进了近期文献中的一些结论.First, we introduced KKM theorems in the linear topological space, then we established some new generalized KKM-type theorems based on weakly generalized KKM mapping without any convexity structure in topological spaces, saddle point theorems and an existence theorem of Nash equilibrium were proved in non-compact topological spaces. The results presented in paper unified and generalized some known results in recent literature.

关 键 词：弱广义KKM映射 弱广义对角拟凸 鞍点定理 NASH平衡 

分 类 号：O177.91[理学—数学]