凸函数的扩充单调性及其在积分上应用

The Extended Monotonicity of the Convex Function and Its Application on Integrals

讨论了凸函数的连续性和有界性,定义了扩充单调的概念,以此为基础给出了开区间内和闭区间内凸函数的扩充单调性质,并将该性质应用在可积函数上,得到了一个判断n阶积分的凸性和单调性的方法.

First, the continuity and boundedness of convex functions are discussed and the concept of extended monotone is defined. Based on this, the extended monotonicity of convex functions both in open intervals and closed intervals is discussed. A method to judge the convexity and monotonicity of the integral of order n is derived by applying the extended monotonicity to integrable functions.