闭区间上凸函数的单调性与超加性

本文利用凸函数定义,获得了闭区间a,b]上凸函数的有界性、区间端点处的极限存在性以及闭区间0,c]上凸函数对于数乘运算的不等式性质,进而利用连续延拓的方法构造了a,b]上的连续凸函数,给出区间a,b]上凸函数的单调性,最后给出区间0,c]上凸函数满足超加性的一个充分条件.

Monotonicity and Superadditive of Convex Function on Closed Interval

By means of the defmition of convex function, the boundedness, the limit existing on the end of interval and the nature of inequality of the number rides operation on interval 0, c] were received. And then, with the method of continuous continuation to build a continuous convex function on interval a, b], the monotonieity of convex function on interval a, b]was provided, and a sufficient condition of convex function become superaddtive function was given.