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二元凸函数与不等式

时间:2017-08-11 数学毕业论文 我要投稿

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

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