对数均值不等式的证明、应用及延伸  

Proof,Application and Extension of Logarithmic Mean-Value Inequality

作　　者：施俊 SHI Jun(School of Mathematics and Physics,Jiangsu University of Technology,Changzhou 213001,PRC)

机构地区：[1]江苏理工学院数理学院,江苏常州213001

出　　处：《高等数学研究》2021年第6期55-58,48,共5页Studies in College Mathematics

基　　金：江苏理工学院教改项目:单招生高等数学教学内容研究与教材建设(编号:11611211821).

摘　　要：给出了对数均值不等式的多种变形形式和三种证明方法,分析了各种证法的特点,并举例说明了该不等式的部分应用,显示了其在证明不等式方面的简洁性,然后运用该不等式推导出几个重要结论,显示了该不等式的重要性和优越性.In this paper,several deformations and three proofs of logarithmic mean-value inequality are presented,the characteristics of the proofs are analyzed,some applications of the inequality are illustrated,showing the simplicity in proving the inequality,and several conclusions are derived,showing the importance and superiority of the inequality.

关 键 词：对数均值不等式 柯西中值定理 极限 延伸 

分 类 号：O171[理学—数学]