摘要
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.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第15期191-197,共7页
Mathematics in Practice and Theory
关键词
E-凸集
E-凸函数
E-拟凸函数
稠密
闭性
(弱)近似凸性
上(下)半
连续
E-convex sets
E-convex functions
E-quasi convex functions
density, closeness
(weak) nearly convexity
upper(lower) semi-continuous functions