摘要
首先给出了集合A={λ∈[0,1]:f(λE(x)+(1-λ)E(y))max{f(x),f(y)},E(x),E(y)∈M}的稠密性证明,然后利用此引理并在E:Rn→Rn为线性映射,f:M Rn→R为上半连续的条件下,给出了拟半E-凸函数的一个新的充要条件,从而简化了对拟半E-凸函数的判别,为进一步认识和研究E-凸函数、半E-凸函数、拟半E-凸函数及其他广义凸函数提供了新的思路。
Firstly, the proof of the density of set is given. By the lemma and the conditions which maps are linear, functions are upper semi - continuous, a necessary and sufficient condition of the quisi - semi - E - convex functions is given. Thus the verification of quisa - semi - E - convex is simplified. So it offers a new ider about studying E - convex founctions, semi - E - convex founctions, quisi - semi - E - convex founcfions and other general convex functions.
关键词
凸集
E-凸集
稠密性
上半连续
拟半E-凸函数
convexity
E - convexity
density
upper semi - continons
quasi - semi - E - convex functions
