一般化凸空间上的一个连续选择定理(英文)  

A CONTINUOUS SELECTION THEOREM ON GENERALIZED CONVEX SPACE

作　　者：肖刚[1] 

机构地区：[1]韩山师范学院数学与信息技术系,广东潮州521041

出　　处：《数学杂志》2012年第2期249-252,共4页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(60574075)

摘　　要：本文研究一般化凸空间上的连续选择定理.利用在D■X的条件下,一般化凸空间(X,D;Γ)上Γ-凸子集的概念,得到了两类一般化凸空间之间,以及φ映射和Γ-凸映射之间的关系,并且得到了一个连续选择定理.本文推广了一般化凸空间上凸子集的概念.In this artilce,we discuss a continuous selection theorem on generalized convex space.Using the definition of Γ-convex set in a generalized convex space（X,D;Γ）,where D is not necessarily a subset of X,we get the relationship between generalized convex spaces with DX and generalized convex spaces with D X,as well as the relationship between Φ-map and a multimap with nonempty Γ-convex values.Moreover,we also get a continuous selection theorem.We extend the conception of Γ-convex set in the generalized convex space.

关 键 词：一般化凸空间 Γ-凸子集 Φ映射 连续选择定理 

分 类 号：O177.91[理学—数学]