向量均衡问题解集的闭性  

Closeness of Solution Sets for Vector Equilibrium Problems

作　　者：龚循华[1] 邹四亚[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（理科版）》2010年第6期511-515,共5页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(10561007);江西自然科学基金资助项目(2008GZS0072)

摘　　要：在实局部凸Hausdorff拓扑向量空间中,先证明在锥的拓扑内部不空的前提下,若满足一定条件,则对称弱向量拟均衡问题的解集是闭集;同时证明了对称强向量拟均衡问题的解集也是闭的;接着,又证明了向量值函数的强鞍点点集是闭集;最后,根据Ky Fan引进的关于三元映射的广义Ky Fan不等式问题,证明了一定条件下其解集也是闭集。First,it proves the closeness of solution sets for symmetric weak vector quasi-equilibrium problems and symmetric strong vector quasi-equilibrium problems satisfying certain conditions in real locally convex Hausdorff spaces;then it proves that solution set of strong saddle points for vector-valued functions is closed;finally,it also proves the closeness of solution set for the generalized Ky Fan inequality problems with trifunctions satisfying certain conditions.

关 键 词：对称弱向量拟均衡问题 对称强向量拟均衡问题 广义Ky Fan不等式问题 强鞍点 闭性 

分 类 号：O317[理学—一般力学与力学基础]