广义度量S-KKM映射的性质及其对鞍点问题的应用(英文)  

The Generalized Metric S-KKM Mapping Principle and the Application to the Saddle Point Problems

作　　者：文开庭[1] 

机构地区：[1]毕节学院数学系,毕节贵州551700

出　　处：《数学进展》2008年第4期409-416,共8页Advances in Mathematics（China）

基　　金：the Scientific Research Foundation of Bijie University.

摘　　要：引入了S为集值映射情况下的广义度量S-KKM映射和超S-γ-广义拟凸(凹)函数,建立了广义度量S-KKM映射原理和广义度量S-KKM映射与超S-γ-广义拟凸(凹)函数的关系.作为应用,获得了超凸度量空间中的新的Ky Fan极大极小不等式和鞍点定理.In this paper, the generalized metric S-KKM mapping and the hyper S-γ-generalized quasi-convex （resp., concave） functional are introduced when S is a set-valued mapping, the generalized metric S-KKM mapping principle is obtained, and the relation between the generalized metric S-KKM mapping and the hyper S-γ-generalized quasi-convex （resp., concave） functional is established. As application, the new Ky Fan minimax inequality and the new existence theorem for saddle points are obtained in hyperconvex metric spaces.

关 键 词：超凸度量空间 次允许集 广义度量S-KKM映射 超S-γ-广义拟凸(凹) 极大极小不等式 鞍点 

分 类 号：O177.91[理学—数学]