1) mean inequality
平均不等式
1.
Based on the popularization of mean inequality,some properties of weighted power mean functions and their applications are discussed.
在推广平均不等式的基础上，讨论了幂平均函数和加权幂平均函数的性质，并简化了一类极限的计算。
2.
As applications of the obtained results,a new proof method about mean inequality is shown.
作为所得结果的应用,给出了平均不等式的一个新证法。
2) average inequality
平均不等式
1.
This paper introduces some interesting examples of applications of average inequality in mathemetical proof.
介绍了平均不等式在数学证明中的几例有趣应用。
3) Power Mean Inequality
幂平均不等式
1.
With the application of Chebyshev inequality and power mean inequality,a series of new generalization of Shapiro inequality and its changes are shown,and some applications of the generalized conclusions are given.
利用Chebyshev不等式和幂平均不等式,研究了Shap iro不等式及其变形的一组新推广,给出了推广结果的一些应用。
2.
By using the Chebyshev inequality and the power mean inequality,a series of new generalizations of Klamkin inequality were studied.
利用Chebyshev不等式和幂平均不等式,研究了Klamkin不等式的一组新的推广,并给出了推广方法和结论的一组应用。
3.
By using Cauchy inequality and power mean inequality, a corrected power generalization of circular inequality and its dual generalization are studied, and the applications of the generalized conclusions are given.
利用Cauchy不等式和幂平均不等式,研究了循环不等式的校正加权推广及其对偶推广,给出了推广结果的应用。
5) geometric average inequality
几何平均不等式
1.
Discrete weighted geometric average inequality;
离散形式的加权几何平均不等式
6) mean inequality
平均值不等式
1.
New Application of Mean Inequality
关于平均值不等式的新应用
2.
In the article,the existence of limit of(an)is proved by using mean inequality,and the result that the proving of boundedness is stronger is got.
运用平均值不等式证明了数列an=(1+1n) n 的极限存在性 ,并且得到有界性比较强的结果。
补充资料：Harnack不等式(对偶Harnack不等式)
Harnack不等式(对偶Harnack不等式)
quality (dual Hatnack inequality) Harnack in-
【补注】一直到G的边界的H助nack不等式，见【AZI.l翻..‘不等式(对停H山丸朗k不等不)[ Har.改沁-勺函勺(d切红Hat’I犯‘k如为uaJ卿);rap.姗二p魄HcT助(月加湘oe)] 给出正调和函数的两个值之比u(x)/“(y)的上界和下界估计的一个不等式，由A.Hai，剐火(汇IJ)得到.令u)0是n维E议当d空间的区域G中的一个调和函数;令E。(y)是中心在点y处半径为;的球{x:}x一y!<;}.若闭包万了刃.CG，则对于所有的、“凡(，)，o
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条