锥凸集值映射的基本性质

Basic Properties of Cone Convex Set-Valued Maps

本文首先在R^m的幂集上定义了一种锥序关系并借助这种序关系定义锥凸集值映射,证明了普通单值凸函数的一些基本性质拓广到这种锥凸集值映射时仍成立.

In this paper,we give difinitions concerning cone ordering on the power sets of R^m,define the cone convex set-valued maps and discuss the properties of the cone convex set-valued maps by using the definitions and the properties of the cone ordering. We show that the cone convex set -valued maps still retain many basic properties of real convex functions.