ON OPPENHEIM＇S INEQUALITY

We prove several inequalies for symmetric postive semidefinite, general M-matrices and inverse Mmatrices which are generalization of the classical Oppenheim‘s Inequality for symmetric positive semidefinite matrices.     

关于两个新型Hilbert不等式的推广

众所周知,Hilbert不等式是一个有重要应用的不等式,1998年,B．G．Pachpatte给出了类似Hilbert级数不等式的两个新不等式,本文的主要工作是推广了这两个新个新不等式。     

Radon不等式的新推广

利用Ho。lder不等式、Young不等式、Chebyshev不等式、幂平均不等式建立Radon不等式的指数推广形式,得到一个具有广泛应用价值的不等式.指出文[7]中给出的关于Radon不等式的推广结果是错误的,并在本文中作了修正.     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的Holder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式，而在于发现新的不等式．     

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。     

关于Polya-Szegoe不等式

本文给出两个改进的不等式,使改进后的每一个新的不等式均含有Polay-Szeg（o）两个不等式改进在内.     

对偶Brunn-Minkowski不等式的逆

20世纪80年代Milman曾指出:反向Brunn-Minkowski不等式是凸几何的一个深刻的结果.考虑了对偶情况,建立了一个反向的对偶Brunn-Minkowski不等式.进一步,均值积分差的反向对偶Brunn-Minkowski型不等式也被建立.     

哈代不等式的一个注记

利用H■lder不等式证明Hardy不等式在p<0时成立,并给出Hardy不等式的应用.     

反向Dresher不等式

配合使用Houlder不等式和Minkowski不等式,得到了反向Dresher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。     

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.     

A note on Hardy-type inequalities

We use a theorem of Cartlidge and the technique of Redheffer's ``recurrent inequalities" to give some results on inequalities related to Hardy's inequality.

     

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.     

On general Bernstein and Nikol’ski type inequalities

The goal of this paper is to establish the relations between general Bernstein and Nikol’ski type inequalities under some weak conditions. From these relations some known classical inequalities are implied. Also, a family of functions equipped with Bernstein type inequality which satisfies Nikol’ski type inequality is found.     

关于广义变分不等式与广义拟变分不等式

本文在非常一般的框架下,建立了极大极小不等式,广义变分不等式和广义拟变分不等式,证明了解的存在定理,且它们是在非紧集上得到的,从而推广和改进了[3～13]中的相应结果.     

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.     

短阵乘积和重排不等式的推广

In this paper, some inequalities for sequence rearrangement and matrix product areestablished. The authors extend and improve some known results, and show that there aresome errors in reference on inequalities for sequence rearrangement by examples,     

Some Hardy-Type Inequalities

In this paper, some new Hardy-type inequalities involving many functions are obtained. These on the one hand generalize and on the other hand improve some existing results by Isumi and Isumi, Levinson, and Pachpatte on this famous type of inequalities.     

Functional inequalities for the Wright functions

In this paper, our aim is to show some mean value inequalities for the Wright function, such as Turán-type inequalities, Lazarevi?-type inequalities, Wilker-type inequalities and Redheffer-type inequalities. Moreover, we prove monotonicity of ratios for sections of series of Wright functions, the result is also closely connected with Turán-type inequalities. In the end of the paper, we present some other inequalities for the Wright function.     

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.