用二元均值不等式的变形式给出两个分式不等式的推广及证明。
Two proofs based on two lemmas for average inequality was discussed in this paper.
利用控制不等式理论简洁地证明了一些整幂函数不等式，大部分结果是一些常用不等式的推广。
By means of the theory of majorization, some inequalities with the integer power function simply are proved, and most of results is extension of applied inequalities.
第二部分将通常的积分平均值不等式推广成一般形式，并利用它给出一些不等式的证明。
The part two general forms was derived with general integral average inequality and Some inequality was proved with this result was obtained above.
文章利用几何凸函数的性质推广了一类重要的和式不等式，得到了一些新的结论。
In this paper, We availed the property of geometic convex function generalized a kind of important sum inequality and obtained some new conclusions.
利用数形结合的思想为不等式构造解析几何模型，并加以推广。
This article structures and extends an analytic geometry model for a inequation based on combining Numbers and shapes.
推广了经典的柏努利不等式，获得了一些新结果。
This paper generalized the classical Bernoulli inequality and obtained some new results.
与此同时推广了平行四边形法则，给出了一些重要的算子不等式。
Moreover, the parallelogram law is also generalized and some important operator inequalities are established.
分别给出含根式的一个几何不等式和一个代数不等式的指数推广。
This paper intends to give the generalization with exponent respectively about a geometric inequality and an algebraic inequality containing radical expression.
提出了函数的双参数加权平均的定义，证明了一个凸函数的双参数加权平均不等式，加强和推广了有关文献中的结果。
The two - parameters weighted mean in defined and an inequality for two - parameters weighted mean of convex function is prove, they have generalized and improved the results in literatures.
本文把有限个数的调和、几何、算术加权平均值不等式推广到无穷多个数的形式和广义积分的形式。
In this paper, we prove the infinite weighted mean inequalities. Furthermore, some results are established in infinite integral case.
建立几个新的具有幂非线性的离散不等式，它们推广并统一了B 。
Some new discrete inequalities with the power nonlinearity are obtained which unify and generalise some known results due to B.
借助一个重要的不等式研究一类带有强迫项的时滞差分方程的振动性，并推广至高阶的情形。
An important inequality is used to establish some criteria for the oscillation of forced difference equation and it is generalized to higher order.
证明了几个与四元数矩阵迹有关的弱控制不等式，推广、改进了有关文献的相应结果。
Several weakly controled inequalities with relation to trace of quaternions matrices are proved, and relevant results in some references are generalized and improved.
给出了幂平均不等式及其推广、二维加权幂平均不等式等的构成函数，并讨论了它们的单调性。
This paper discusses the generating functions of monotony for the Power-Mean Inequality, Binary dimension power mean inequality and Binary integral power mean inequality.
给出了凸函数的一个积分性质的推广，并由此得到了凸函数的几个积分不等式。
An integral property of the convex function is generalized, and the some integral inequalities of the convex function are given.
给出了两个拓扑向量空间的乘积空间上截口定理，极小极大不等式及一个推广的不动点定理。
A section theorem, a minimax inequality and a generalized fixed point theorem where the underlying space is a product space of two topological vector Spaces, are given.
作为应用，建立它的等价形式及对应二重级数的最佳推广不等式。
As applications, we build its equivalent form and the analogue general double series inequalities.
对一个无理不等式从多方面给出推广和引申，得到一类新颖、有趣的无理不等式。
In this paper, an irrational inequality is generalized and extended in many-sided, a class of new irrational inequalities are established, which are interesting and useful.
本文利用分析方法及不等式理论 ，建立了杨乐不等式及其推广与加强的探微形式 。
In this paper, we extablish subtle exploration forms of Yang Le inequality and its extension and strength, by using the method of analysis and theory of inequalities.
将著名的一元控制不等式推广到多元的情形，获得了一个重要的多元凸函数的控制不等式。
The well-known majorizing inequality is generalized to space of higher dimensions, and a important majorizing inequality is obtained.
利用平均值不等式，得到高次齐次函数的若干条件不等式，推广了低次齐次函数的相关结果。
In this paper, we through the example introduce some applications of the mean value inequality in mathematical analysis.
这个不等式是经典结果的推广，它可被用来研究积分性质和用来做积分值的估计。
This generalized inequality of the classic result can be used to estimate the integral value, or study the quality of the calculus.
作者得到了粗糙核分数次积分算子的两权弱型不等式，推广了Cruz-Uribe和Perez的结果。
The authors give the two-weight weak-type inequality for the rough fractional integral operator, which is an extension of result obtained by Cruz-Uribe and Perez.
作者得到了粗糙核分数次积分算子的两权弱型不等式，推广了Cruz-Uribe和Perez的结果。
The authors give the two-weight weak-type inequality for the rough fractional integral operator, which is an extension of result obtained by Cruz-Uribe and Perez.
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