关于凸函数的定义和性质

On the Definition and Properties of Convex Function

通过对凸函数定义和性质的研究,得到了多个与凸函数定义不等式等价的式子,方便了凸函数的判定,给出了应用凸函数性质证明不等式的例证。

By studying the definition and properties of convex function, this paper gets many formulas which are equivalent to the inequalities defined by the definition of convex function. These formulas in turn help define convex function. This paper also gives examples which show that inequalities can be proven by the properties of convex function.