王乃泽+论文定稿.docVIP

本科毕业设计（论文） ( 2013 届 ) 题 目： 不等式的证明及其运用 专 业： 班 级： 姓 名： 学 号： 指导教师： 职 称： 完成日期： 不等式证明及其运用 王乃泽 （温州大学学院，浙江温州，325027）Inequality proof and its application Wangnaize Oujiang College, Wenzhou University，Wenzhou, Zhejiang，325027 Abstract：Inequality proof and its application in mathematics has a indispensable role and status, from elementary mathematics to higher mathematics, inequality has been and we were like peas and carrots, its application range is very wide, is an important part of the capacity of mathematics teaching. In the inequality proof process need to use many mathematical thought, combined with many important mathematical content, this paper mainly introduces several famous between inequality proof, use, and contact, help you distinguish between solve how to reasonably and effectively use the inequality to achieve their desired expected effect. These a few inequality is we often in the study will use, concrete, it is through the convex function related definition and nature, and then introduce Jensen inequality, Jensen inequality is derived by the holder inequality, from holder inequality we see, as long as everyone is a widely known as the deformation of Cauchy inequality. And Cauchy inequality is discussed in this paper the key content, we will mainly discuss the Cauchy inequality several main forms and relevant proof, examples of application and so on. After that we will through the Cauchy inequality is famous mean inequality, from mean inequality back to Jensen inequality related content. So far, this paper discusses the important content. Keywords: convex functions; Inequality; 目录 前言 4 1 凸函数的性质及其应用 5 1.1凸函的定义及性质 5 1.2 由Jensen不等式推导holder不等式的相关证明 7 2 柯西不等式 9 2.1柯西（Cauchy）不等式 9 2.1.1柯西不等式几何证明 9 2.1.2柯西不等式的主要形式 10 2.2柯西不等式的应用举例 14 2.2.1应用柯西不等式求最值 14 2.2.2柯西不等式推导点到直线的距离公式 15 2.2.3柯西不等式