关于一类E-凸集的判别准则

On criteria of a kind of convex sets

首先给出了集合A={λ∈[0,1]:E(y)+λ(E(x)-E(y))∈x, x,y∈x}的稠密性证明,然后利用此引理并在映射E:RnRn为连续映射的条件下,给出了一类E-凸集合的一个充要条件,这样将集合E-凸性的验证转化为验证对某一个λ∈(0,1),λEx+(1-λ)Ey∈x是否成立,简化了该类E-凸集合的判别.

Firstly,the proof of the density of set is given .By the lemma and the conditions which maps are continuous, a necessary and sufficient condition of a kind of the convexity of the sets is given .Thus the verification of the kind of convexity becomes the problem which is right or not and the verification of the kind of convexity is simplified.