Cauchy-Schwarz不等式的应用及推广  

The Application and Extension of Cauchy-Schwarz's Inequality

作　　者：林越[1] 

机构地区：[1]琼州学院理工学院,海南三亚572022

出　　处：《琼州学院学报》2012年第5期7-9,共3页Journal of Qiongzhou University

基　　金：三亚市院地科技合作项目(2012YD29)

摘　　要：Cauchy-Schwarz不等式是异于均值不等式的另一个重要不等式,不仅在数学分析、高等代数中应用比较广泛,在竞赛数学和工程实际计算中也有广泛的应用.研究Cauchy-Schwarz不等式的几种特殊形式,并分别给出了它们的证明,最后给出了Cauchy-Schwarz不等式的推广形式.The cauchy - Schwarz＇ s Inequality is a importom inequality different by Mean Vaule Inequality. It＇ s not only wide application in Mathematical Analysis and Higher Algebra, and also used in the competition mathe- matics and engineering calculation. In this article,we main researched some of special form of cauchy - Schwarz＇ s Inequality, and gived the proof of them. In the end, we get the extension from of the The cauchy - Schwarz＇ s Inequality.

关 键 词：CAUCHY-SCHWARZ不等式 均值不等式 HOLDER不等式 辅助函数 

分 类 号：O15[理学—数学]