摘要
作为集合凸性概念的一种推广以及统一凸性与近似(nearly)凸性等概念的一种尝试,本文引入集合?-凸性的概念,并对?-凸集合的性质进行初步的研究.另外,本文还研究了一些常见变换与集合运算的保?-凸性质.
In this paper, the concept of Ω-convexity of sets in linear spaces is introduced as a generalization of the classical convexity and as an attempt to give a uniform treatment of the classical convexity and the near-convexity etc. The basic properties of Ω-convex sets are investigated and some operators/compositions on sets, which preserve the Ω-convexity of sets, are studied.
出处
《应用数学》
CSCD
北大核心
2017年第4期850-855,共6页
Mathematica Applicata
基金
Supported by the National Natural Science Foundation of China(11671293,11271282)
关键词
Ω-凸性
凸性
近似凸性
保凸性
中点凸性
Ω-convexity
Convexity
Near convexity
Convexity-preserving
Middle-point convexity
