应用Cauchy-Schwarz不等式证明积分不等式举例  

Using Cauchy-Schwarz Inequality to Prove Integral Inequalities

作　　者：吴克坚 刘烁 徐清华 王瑞星 赵清波 WU Kejian;LIU Shuo;XU Qinghua;WANG Ruixing;ZHAO Qingbo(Department of Mathematics & Physics, School of Basic Medicine, Air Force Medical University, Xi'an 710032 China)

机构地区：[1]空军军医大学基础医学院数学物理教研室,陕西西安710032

出　　处：《高等数学研究》2021年第2期13-15,54,共4页Studies in College Mathematics

基　　金：空军军医大学基础医学院《人才建设行动计划》公共教研室骨干人才.

摘　　要：本文主要以近年大学生数学竞赛的两道典型题目为例,说明Cauchy-Schwarz不等式在证明积分不等式中的应用.这些题目的不同解法既体现了普遍适用性也体现了技巧的针对性,对教师的教学和学生的学习提供帮助.This paper mainly analyzes two classical applications of using Cauchy-Schwarz inequality to prove some integral inequalities appeared in the Mathematics Competitions in recent years,and shows the universality of the corresponding methods and the relevance of some techniques.We hope to provide useful help for teaching and learning.

关 键 词：CAUCHY-SCHWARZ不等式 积分不等式 数学竞赛 

分 类 号：O13[理学—数学] O178[理学—基础数学]