E-凸函数和E-拟凸函数的等价条件

Equivalent Conditions for E-Convex Functions and E-Quasi Convex Functions

在更弱的连续假设下研究集合A_(x,y)={λ∈[0,1]|f(λE(x)+(1-λ)E(y))≤λf(E(x))+(1-λ)f(E(y))}和集合A′_(x,y)={λ∈[0,1]|f(λE(x)+(1-λ)E(y))≤max{f(E(x)),f(E(y))}}的稠密性、闭性、(弱)近似凸性,得到E-凸函数和E-拟凸函数的等价条件.

In this paper, the density, closeness and （weak） nearly convexity of the setsAx,y={λ∈[0,1]｜f（λE（x）＋（1-λ）E（y））≤λf（E（x））＋（1-λ）f（E（y））} and Ax,y={λ∈[0,1]｜f（λE（x）＋（1-λ）E（y））≤max{f（E（x））,f（E（y）））} are investigated, some equivalent conditions for E-convex functions and E-quasi convex functions are derived under the weaker continuity assumptions.