七种锥拟凸向量函数间的关系

THE RELATIONS OF SEVEN KINDS OF CONE QUASICONVEX VECTOR FUNCTIONS

锥拟凸向量函数的概念是通常实值函数拟凸性的拓广。由于拓广途径不一 ,在许多有关文献中各自提出了自己的锥拟凸向量函数概念。本文综述了文献中出现的七种锥拟凸向量函数的概念并着重讨论它们之间的关系 ,结果发现这七种锥拟凸向量函数的定义有些是等价的 ,有些是存在某种包含关系。针对那些不等价的定义 。

This paper summarizes several different definitions of cone quasiconvex vector functions proposed in different literatures and discusses the relations among them.The conclusions in this paper indicate that some of these definitions of cone quasiconvex vector functions are equal,some are different.Moreover,some examples are adduced for these unequal definitions of cone quasiconvex vector functions.