闭区间上凸函数的单调性与超加性

Monotonicity and Superadditive of Convex Function on Closed Interval

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.

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.