向量均衡问题解集的闭性

Closeness of Solution Sets for Vector Equilibrium Problems

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.