幂平均不等式

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。

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 .

从均值不等式、幂平均不等式出发，通过构造矩阵和利用文的结果，证明了一类和式不等式，并推广了幂平均不等式。

Based on the mean value inequality and power mean inequality and with structural matrixes and the result of thesis [ 1 ] , this essay proves a class of sum inequalities and promotes the power mean inequality .

将文[1]的加权Carlson不等式推广为二元积分幂平均不等式。

In this paper , the power Carlson inequality in the reference [ 1 ] is generalized into binary integral power mean inequality .

幂平均不等式的改进及在凸性模估计中的应用

Improvement of the Power Mean Inequality and Applications in Estimation of Convexity Modulus

关于算术-幂平均不等式的加细

On refinement of the arithmetic - power mean inequality

幂平均不等式的最优值

On the Optimal Values for Inequalities Involving Power Means

关于广义幂平均不等式（Ⅰ）

About the Inequalities of Generalized Powers Average (ⅰ)

由幂平均不等式引发的猜想

Conjectures Aroused From the Tower Mean Inequality

关于凸函数和凹函数的幂平均不等式的一个注记

A Note On Mean Value Inequality of The Power about the Convex Function and Concave Function

最后，我们应用所得结果给出加权幂平均不等式以及加权平均不等式的加细形式。

Finally , we provide an application of obtained result to the refinement of weighted power means inequality and weighted means inequality .

对加权幂平均不等式的加强作了全面的研究，推广了一个加强的加权算术-几何不等式。

We make a comprehensive study to the sharpening of inequality related to weighted power means which generalizes a sharpening of the weighted arithmetic-geometric inequality .

本文研究了正数方幂平均不等式，得到了若干个新结果，从而改进了文〔1,2〕的相应结果。

The paper discusses the power mean inequalities of positive numbers and gets some new results . Thus we improved the relevant results of the paper 〔 1,2 〕

广义Heron平均和幂平均的不等式

The Generalized Heron Meron Mean and Power Mean Inequalities

正定Hermite矩阵加权幂平均的行列式不等式

Weighted Power Mean Inequality of Determinants for Positive Definite Hermite Matrices

混合幂均差函数对平均不等式的隔离

Isolate of mean inequality resulting from mixed differences function of power means

几个幂指函数不等式及其证明幂平均不等式的最优值

Some Inequalities for Power-exponential Functions On the Optimal Values for Inequalities Involving Power Means