函数的凸性及其判别的充要条件

The convex function and its necessary and sufficient condition

本文给出凸函数的一个等价定义,并证明在区间(a,b)内凸的f(x)是连续的,最后证明了在存在f″(x)时,f(x)在(a,b)内凸当且仅当f″(x)>0。

In this paper, we give a new equivalent definition of the convex function. We also prove that the convex functionf（x）defined on （a, b） is continuous and furthermore, when f′（x） exists,f （x） is convex if and only if f′（x）〉0.