凸函数的等价定义及几何特征

The equivalent definition and geometric characteristics of convex function

从凸函数的基本概念出发,在此基础上引申出了凸函数的等价定义,并通过例题说明了凸函数的定义及等价定义在证明不等式中的应用.讨论了凸函数几何特征,并以实际算例介绍了凸函数的几何性质的应用,对凸函数研究有一定的应用价值.

Starting from the basic definition of convex function, this article extends the equivalent definition of convex function. The application of convex function definition and its equivalent definition in proving inequality are explained by examples. At the same time, the geometric characteristics of convex function are discussed, the application are introduced through examples. It has some value in convex function research.