半连续性与一致不变凸函数  

Semicontinuity and uniformly invex functions

作　　者：杨玉红[1] 赵克全[1] 吴欧[1] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047

出　　处：《重庆工商大学学报（自然科学版）》2006年第1期8-10,共3页Journal of Chongqing Technology and Business University:Natural Science Edition

摘　　要：作为对凸函数的推广,1983年Zalinescu提出了一致凸函数的概念,并讨论了它们的一些性质特点;1998年Yang在上半连续和下半连续条件下给出了一致凸函数的一些等价条件,简化了一致凸性函数类的判别条件。在此基础上,首先提出一致不变凸函数的概念,借助Neogy等人所引入的条件C以及Yang所引入的条件D,并利用Yang的思想,分别在上半连续和下半连续条件下给出了一致不变凸函数的几个判别准则,简化了一致不变凸性函数类的判别条件,是Yang的结果的相应推广。To generalize convex functions, Zalinescu introduced the concepts of uniformly convex functions in 1983, and discussed some properties for them;under the conditions of upper semicontinuity and lower semicontinuity, some equivalent conditions were given by Yang in 1998, so that criteria for uniformly convex functions are simplified. Based on the above,in this paper, firstly the concepts of uniformly invex functions are given;then according to Yang＇s idea,under the conditions of upper semicontinuity and lower semicontimuity respectively, some criteria for uniformly invex functions are obtained by using the condition C introduced by Neogy and the condition D introduced by Yang;therefore, criteria for uniformly invex functions are simplified and Yang＇s conclusions are generalized correspondingly.

关 键 词：凸集 一致凸函数 不变凸集 一致不变凸函数 半连续性 

分 类 号：O174.4[理学—数学]