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

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.