关于凸函数的连续性的一些结果

Some Results About Continuity of Convex Function

凸函数是数学分析中的一类重要函数,而函数的连续性又是函数性态的一项基本而又重要的特征.文章从凸函数的定义出发,讨论了凸函数与连续的关系,得出了连续函数不一定是凸函数,凸函数也不一定连续的结论,给出了判别连续凸函数的几个充要条件及连续凸函数的几条特殊性质.

The convex function is very important in mathematical analysis and the continuity is the elementary and vital feature of the function.On the Basis of the definition of the convex function,this paper discussses the relationship between convex functions and the continuity and concludes that the continuous functions are not necessarily the convex functions,and the convex functions are not necessarily continuous.The necessary and sufficient conditions are presented to judge a continuous convex function and the its special nature is introduced.