摘要
对凸集概念作了进一步推广。首先定义了向量值函数F:K×K×[0,1]→R^n是K■R^n上的广义凸结构概念,并给出了广义凸结构的一个性质,进而定义关于广义凸结构F的凸集、近似凸集、弱凸集3种广义凸集概念,并给出这3种广义凸集等价刻划,证明了闭的关于F的弱凸集是关于F的凸集。
This article extends the concepts of convex sets. We consider a definition of a vector-valued function F：K×K×[0,1]→R^n K■R^nwhich is a generalized convex structure over K R^n , and introduce a property of it. Furthermore, we give the concepts of convex, nearly convex and weakly convex sets with respect to F, and give the equivalent propositions, respectively. We prove that a closed weakly convex set with respect to V X,YE K is convex with respect to V X,YE K.
出处
《重庆师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2016年第1期6-12,共7页
Journal of Chongqing Normal University:Natural Science
基金
黑龙江省教育厅科学技术研究项目(No.12531684)
佳木斯大学科学技术研究重点项目(No.12Z1201517)
关键词
广义凸结构
广义凸集
凸集
近似凸集
弱凸集
generalized convex structure
generalized convex sets
convex sets
nearly convex sets~ weakly convex sets
