广义凸函数的特征性质

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一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 Characteristic Properities of Generalized Convex Functions

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.