二元凸函数与不等式

2元凸函数与不等式

摘要：凸函数有许多特性，本文给出了2元凸函数的3种不同定义，证明了3种定义间的等价关系，推广了琴生不等式，建立了2元凸函数的判定定理，最后举例说明了2元凸函数在证明著名不等式及初等不等式方面的应用。

关键词：2元凸函数；平面开凸域 ；判别法；不等式

Two—variable Convex Function and Inequality

Abstract: Convex function possesses a great number of specific properties.This article presents the three kind of different definition of two—variable convex function,and also proves equal relations during three kind of different definition,popularizes Jensen s inequality and establishes the decision theroem of two—variable convex function,finally illustrates with examples that two—variable convex function certificates the famous inequality and the primary inequality.

Keywords: two—variable convex function ;Plane open convex region;Decision methods;Inequality