抽象凸空间中广义最大元的稳定性

Stability of the Generalized Maximal Elements in an Abstract Convex Space

在满足H0-条件的抽象凸空间中,利用一个集值映射来表示广义最大元的全体,将广义最大元的稳定性问题转化为研究该集值映射的连续性问题.最后借助Fort定理,证明了该集值映射是连续的,从而解决了抽象凸空间中广义最大元的稳定性问题.

By using a set-valued mapping,this paper expresses all the maximal elements in an Abstract convex space which satisfies H0-condition and hence converts the stability problem of generalized maximal elements into a continuity problem of the set-valued mapping.Finally,by using Fort theorem,it works out a proof of continuity of the set-valued mapping under certain conditions and so gives out a resolution of stability problem of the generalized maximal elements in an Abstract convex space.