平均不等式及其应用推广的研究

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1、平均不等式及其应用推广的研究数学专业学年论文摘要各种各类的平均值在我们生活之中的运用到处可见，本文主要介绍了几种常用的平均值的意义及应用，还有对平均值不等式以及与其相关的重要不等式的证明和推广作讨论，最后通过例题证明了解平均不等式的综合运用。关键词平均值平均值不等式AbstratAllkindsofaveragevalueareusedinourlives.Thispapermainlyintroducesthemeaningsandapplicationsofseveralcommonmeanvalue,anddiscussthepromotionandex

2、tensionaboutTheMeanValueInequalityanditsrelatedimportantinequalities.Finallyitletsusknowthecomprehensiveuseofaverageinequalitythroughsomeexamples.Keywords：MeanValueInequality目录1引言........................................................................................................

3、............................12几种常用的平均值............................................................................................................22.1算术平均值................................................................................................................22.2几何平均值.......

4、.........................................................................................................22.3调和平均值................................................................................................................42.4平方平均值................................................

5、................................................................52.5对数平均与加权平均值............................................................................................63平均值不等式的介绍......................................................................................................

6、..83.1平均值不等式一般定理............................................................................................83.2平均值不等式一般表达式的证明............................................................................83.3加权平均不等式及其推广..................................................................

7、....................104.与平均值不等式相关的几个重要结论.........................................................................124.1柯西不等式..............................................................................................................124.2切比雪夫不等式......................................

8、...................