KKM相关定理的证明  

The proof of some results about KKM mapping

作　　者：杨春艳 Yang Chunyan(Division of Mathematics,Sichuan University Jinjiang College,Pengshan Sichuan 620860)

机构地区：[1]四川大学锦江学院数学教学部,四川彭山620860

出　　处：《科学咨询》2020年第40期33-34,共2页

基　　金：四川省教育厅项目基金的支持(80303-AZW003)。

摘　　要：本文证明了Hilbert空间的有界闭凸子集M的一个结论,当且仅当:<L(y),y-x0>≥0,任意的y∈M时,<L(x0),y-x0>≥0,任意的y∈M,紧接着证明了:P:M→2M且P(y)={x∈M,<L(x),x-y>≤0},任意的y∈M,对于映射P就为一KKM映象。这对KKM定理的理解和应用给出了清晰的方法。in this paper,we first define KKM mapping and obtain KKM Theorem and FKKM theorem.Each FKKM is weakly compact and its intersection is not empty.Then the definition of semi-continuity and monotonicity is given.On this basis,a conclusion of bounded closed convex subset M of Hilbert space is proved.If and only if:<L(y),y-x0>≥0,any y∈M,<L(x0),y-x0>≥0,any y∈M,then it is proved that:P:M→2M,P(y)={x∈M,<L(x),x-y>≤0},Any y∈M.For a mapping P,it is a KKMmapping.This gives a clear method for the understanding and application of KKM Theorem.

关 键 词：HILBERT空间 KKM影像 闭凸 

分 类 号：O17[理学—数学]