广义凸函数的特征性质  

The Characteristic Properities of Generalized Convex Functions

作　　者：赵宇[1] 黄金莹[1] 康兆敏[1] 

机构地区：[1]佳木斯大学理学院数学系,黑龙江佳木斯154007

出　　处：《大学数学》2011年第6期105-110,共6页College Mathematics

基　　金：黑龙江省教育厅科学技术研究资助项目(11551499)

摘　　要：提出广义凸集、广义凸函数、中间点广义凸函数、端点广义凸函数四个定义,通过定义条件P1,研究条件P1所蕴含的等式关系,进而得到一个基础性定理—稠密性定理和一个相对条件较弱的推论,最后将结果应用于若干不同类型的广义凸函数类,尤其是s-凸函数、几何凸函数、rp-凸函数,得到它们所共有的一个特征性质,即满足稠密性定理.The author gives four definitions, that is generalized convex sets, generalized convex functions, intermediate-point generalized convex functions and endpoint generalized convex functions. Through define condition P~, the author study the equality relation which be contained with conditon P1. Furthermore, the author obtains a basic theorem-den^sity theorem and a lemma which condtion is relative weaker. At last, the author put these results on some different types of generalized convex functions such as s-convex functions, geometric convex functions and rP-convex functions. We will find that these generalized convex functions have a common characteristic properities, that is they satisfy the density theorem.

关 键 词：广义凸集 广义凸函数 中间点广义凸函数 端点广义凸函数 条件P1 稠密性定理 

分 类 号：O174.13[理学—数学]