On several new Hilbert-type inequalities involving means operators

In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.     

离散型Carlson's不等式的一些推广及改进

In this paper, we consider Carlson type inequalities and discuss their possible improvement. First, we obtain two different types of generalizations of discrete Carlson's inequality by using the Hlder inequality and the method of real analysis, then we combine the obtained results with a summation formula of infinite series and some Mathieu type inequalities to establish some improvements of discrete Carlson's inequality and some Carlson type inequalities which are equivalent to the Mathieu type inequalities. Finally, we prove an integral inequality that enables us to deduce an improvement of the Nagy-Hardy-Carlson inequality.     

关于几个新不等式

本文利用Redheffer不等式,Jordan不等式和Jensen不等式给出了一些新的不等式作为应用推广了文[1]的一个结果。     

一类新的Radon型不等式及其应用

给出一类新的R adon型不等式,它们在代数不等式研究中有着广泛的应用,利用它们可直接得到一大批新的分式型不等式,也可运用它们证明或推广许多不等式.     

类似Hilbert不等式的一些新不等式的推广

本文推广了 Pachpatte在文 [1 ]中给出的类似 Hilbert不等式的一些新不等式 .     

一个不等式的简单证明与推广

本文讨论了一个引人注目而被广泛讨论的、与平均值有关的不等式.我们首先获得了它的完整形式,给出了一个非常简洁而能揭示问题本质的证明.由此我们自然地引出了它的最为一般的形式.同时,我们还指出文献中存在的一些谬误.     

关于一个推广的具有最佳常数因子的Hilbert类不等式及其应用

本文引入单参数λ,对一个Hilbert类不等式作具有最佳常数因子的推广.作为应用,建立它的等价形式并获得了一些特殊结果.     

关于一个Hilbert类不等式及其应用

本文给出一个具有同样最佳常数π的Hilbert类不等式。作为应用，建立其等价形式及导出一些特殊的结果。     

On Variance and Covariance for Bounded Linear Operators

In this paper we initiate a study of covariance and variance for two operators on a Hilbert space, proving that the c-v (covariance-variance) inequality holds, which is equivalent to the Cauchy-Schwarz inequality. As for applications of the c-v inequality we prove uniformly the Bernstein-type inequalities and equalities, and show the generalized Heinz-Kato-Furuta-type inequalities and equalities, from which a generalization and sharpening of Reid's inequality is obtained. We show that every operator can be expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given. Received April 9, 2000, Revised July 20, 2000, Accepted August 8, 2000     

具有多参数的Hilbert型逆向不等式

本文通过引入多个参数和估计权函数的方法,给出了一个具有最佳常数因子的Hilbert型逆向不等式.作为应用,建立了它的等价式并获得了一些特殊结果.     

Short note on Hilbert’s inequality

Considering five different parameters, we obtain some new Hilbert-type integral inequalities for functions f(x), g(x) in L²[0, ∞). Then, we extract from our results some special cases which have been proved before.     

交替方向法求解带线性约束的变分不等式

１引言变分不等式是一个有广泛应用的数学问题,它的一般形式是：确定一个向量,使其满足这里ｆ是一个从到自身的一个映射,Ｓ是Ｒ中的一个闭凸集．在许多实际问题中集合Ｓ往往具有如下结构其中ＡｂＫ是中的一个简单闭凸集．例如一个正卦限,一个框形约束结构,或者一个球简言之,Ｓ是Ｒ中的一个超平面与一个简单闭凸集的交．求解问题（１）－（２）,往往是通过对线性约束Ａ引人Ｌａｇｒａｎｇｅ乘子,将原问题化为如下的变分不等式：确定使得我们记问题（３）－（４）为ＶＩ（Ｆ）．熟知［３］,ＶＩ（,Ｆ）等价于投影方程其中凡（·）表…     

一个Hardy-Hilbert型不等式含多参数的新的推广

In this paper, by introducing some parameters and estimating the weight coefficients, we give a new generalization of Hardy-Hilbert＇s type inequality with the best constant factor. As applications, we consider its equivalent form and obtain some recent results, which are special cases of our results.     

一个新的Hardy-Hilbert类不等式及其应用

本文求出一个具有相同最佳常数因子的类似于Hardy-Hilbert不等式的新不 等式.作为应用,给出它的等价形式及一些特殊结果.     

The logarithmic Minkowski inequality for non-symmetric convex bodies

We validate the conjectured logarithmic Minkowski inequality, and thus the equivalent logarithmic Brunn–Minkowski inequality, in some particular cases and we prove some variants of the logarithmic Minkowski inequality for general convex bodies without the symmetry assumption. An application of one of these variants is shown.     

加权平均值不等式推广到无穷多个数的形式

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。     

Some inequalities involving π and an application to Hilbert's inequality

Some inequalities involving π are proved. As an application, we give some strengthened Hilbert's inequalities.     

含参Schur型排序不等式

本文类比经典的Schur不等式,建立了几个含参Schur型排序不等式,并将其应用于基本Schur型的含参推广.     

On new extensions of Hilbert's inequality

By introducing three parameters A, B and α, and estimating the weight coefficient, we give a new extension of Hilbert's inequality with a best constant factor involving the β function. As applications, we consider the equivalent form and some particular results. This revised version was published online in June 2006 with corrections to the Cover Date.     

Some new results for demimartingales

Harremoёs obtained some new maximal inequalities for non-negative martingales. In this paper, we get some new maximal and minimal inequalities for non-negative demimartingales which generalize the results of Harremoёs. We also obtain an inequality for non-negative demimartingales which generalizes the result of Iksanov and Marynych. Finally we obtain a strong law of large numbers, strong growth rate and integrability of supremum for demimartingales which generalize and improve the result of Chow.