均值不等式

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 .

利用Holder不等式和算术&几何均值不等式，研究了第42届国际数学奥林匹克竞赛的第2题的一个新的隔离推广，并给出了推广结论的应用。

In this paper , with the application of Holder inequality and arithmetic-geometric average inequality , a new segregation and generalization of the second question of No. 42 International Mathematics Olympic is studied , and the application of the generalized conclusion are shown .

均值不等式的一个几何模型及应用

The Geometric Modeling and Usages of Average Inequality

含均值不等式的一些问题及应用

Some Problems and Application of Inequalities with Mean

本文研究了均值不等式在简化初等不等式证明及定积分等方面的一些应用。

Here some applications of average value inequality on the proof of inequality and integral are presented .

均值不等式的两个证法

Two Proofs for Average Inequality

为了能够更好的理解均值不等式，要重视该不等式的证明方法。

Should pay more attention to the proving method of the inequality of average value for better understanding of it . 3 .

均值不等式的应用要符合一定的条件，教师在讲授该知识点时，必须要想办法让学生弄清楚这些条件，这样才能使学生对均值不等式有实质性的了解。

The application of the inequality of average value shall accord with certain conditions . When teaching this point , teachers must make those conditions clear to the students , so that the students could have substantive understanding about the inequality of average value . 4 .

利用已知线性脉冲不等式的研究结果证明了一类非线性的脉冲积分不等式，并利用取指数函数求解积分不等式和均值不等式等方法，给出了一些不等式的精确上界。

The paper proves a class of nonlinear impulsive integral inequalities by means of the result of known linear impulsive inequalities . The exact upper bound of inequalities is given in terms of getting exponential function , solving integral inequality and average inequality and so on .

采用积分均值和微分不等式方法，研究了二维时变Volterra互惠系统的生存状况。

In this paper we study the existence of two-dimensional time-varying Volterra cooperative system by using the methods of integral in mean and differential inequality principle .

T.Ando在文献[7]中给出关于几何均值和调和均值的算子不等式，算子单调函数和算子凸函数的刻画。

T. Ando in [ 7 ] gave some important inequalities on geometric and harmonic means .