摘要
设S是非空集,如果 x,y∈S, α∈(0,1),使得αx+(1-α)y∈S,则称S是弱近似凸集.在本文中,作者证明了闭的弱近似凸集是凸集,并用此结论获得了拟凸函数的一些等价条件.
A nonempty set S is called to be weakly nearly convex if x,y∈S,α∈(0,1) such that αx+(1-α)y∈S. The author proves that a closed weakly nearly convex set is convex, and some equivalent conditions for quasiconvex functions are obtained by applying the results.
出处
《四川大学学报（自然科学版）》
CAS
CSCD
北大核心
2004年第2期226-230,共5页
Journal of Sichuan University(Natural Science Edition)
基金
贵州省教育厅基金(2002301)
贵州大学基金(2001006)
关键词
(弱)近似凸集
闭集
拟凸函数
下半连续
weak) nearly convex sets
closed sets
quasiconvex functions
lower semicontinuity
