凸函数的一个充要条件

A Sufficient and Necessary Condition for Convex Functions

凸函数作为研究凸几何分析的一个重要工具,其凸性的刻画尤为重要。引入Green和Osher给出的一个不等式,利用凸函数的定义证明不等式作为判断函数是凸函数的一个充分必要性条件。引入径向函数刻画星体的定义,给出不等式在星体同一方向上的一个积分型不等式的应用。

Convex function is an important tool in the analysis of convex geometry and it is very important to describe its convexity.An inequality given by Green and Osher is introduced and the definition of convex function is used to prove that the inequality as a judgment function is a sufficient necessary condition for con⁃vex function.The definition of radial function to describe stars is introduced and the application of an integral inequality in the same direction of stars is given.