关于hilbert－ingham不等式和它的应用

本文给出（ｉ）ｈｉｌｂｅｒｔ不等式和ｈｉｌｂｅｒｔ－ｉｎｇｈａｍ不等式一些有意义的共同改进；（ｉｉ）一些ｆｅｊｅｒ－ｒｉｅｓｚ型不等式的改进和（ｉｉｉ）ｈａｒｄｙ不等式的改进．     

积分型Hilbert定理的改进与应用

本文建立如下权函数的不等式ｗ （ｘ） ＝ ∫∞０１ｘ ＋ ｙ ＋ １（ｘ ＋ １ｙ ＋ １）１／２ｄｙ ≤π［１ － １ － ２／π（ｘ ＋ １）１／２］　（ｘ ∈［０,∞））,这里,常数１－ ２／π是最佳值,从而改进了积分型Ｈｉｌｂｅｒｔ定理,作为应用,建立一个Ｈｉｌｂｅｒｔ类积分不等式及其加强式;并改进推广了Ｈａｒｄｙ－Ｌｉｔｔｅｗ ｏｏｄ 积分不等式．     

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.     

关于Hardy－Littlewood－Polya不等式及其应用

此文主要结果是（１）设Ｐ＞１，０＜λ≤１及ｆ（ｘ）（≥０）∈Ｌｐ（０，∞），又设Ｋ（ｘ，ｙ）≥０和［Ｋ（ｘ，ｙ）］１／λ齐负一次式。若有Ｑ＞１，使λ＝２－１／Ｐ－１／Ｑ及　当λ＝１时为Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ－Ｐｏｌｙａ不等式　当λ＝１时为Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ－Ｐｏｌｙａ不等式之一改进。     

Hardy-Hilbert型积分不等式的一种新改进

研究了带积分核函数和参数λ（λ〉1）的Hardy-Hilbert型不等式,并利用加强的Hlder’s不等式对Hardy-Hilbert不等式作了改进,建立了一些新的不等式.     

关于Hilbert积分不等式新的改进和推广

本文通过引入一些常数，运用一些分析技巧和Young不等式，给出了Hilbert积分不等式的一些新的改进和推广。     

一个加强的Carleman不等式

建立如下权系数的不等式：１＋１ｍｍ≤ｅ１－１－２／ｅｍ（ｍ＝１，２，…），这里，１－２／ｅ＝０．２６４２４１１＋为最佳值．从而得到一个加强的Ｃａｒｌｅｍａｎ不等式．     

Cauchy-Schwarz不等式的一些反向及改进

在一些附加条件下给出内积空间的Cauchy-Schwarz不等式的反向不等式及其改进,利用所得结果得到一个新的积分型Kantorovich不等式,并获得关于函数的Fourier系数的两个不等式.     

关于Polya-Szeg(o)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.     

关于Polya-Szeg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-Szego两个不等式改进在内．     

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.     

On the converse Jensen inequality

We give a survey on the converse Jensen inequality and we show that several recently published inequalities are simple consequences of certain long time known results. We also give a new refinement of the converse Jensen inequality as well as improvements of some related results.     

Improvements of the Ostrowski integral inequality for mappings of bounded variation I

In this paper, we establish some improvements of the Ostrowski integral inequality for mappings of bounded variation.     

Extension of Hilbert's inequality

In this paper we make some further extensions of discrete Hilbert's inequality by using Euler-Maclaurin summation formula. We give the improvements of some previously obtained results and also compare our results with some previously known from the literature.     

Improvements of the Ostrowski integral inequality for mappings of bounded variation II

In this paper, we establish some improvements of the Ostrowski integral inequality for mappings of bounded variation.     

Logarithmic Sobolev,isoperimetry and transport inequalities on graphs

In this paper,we study some functional inequalities(such as Poincaré inequality,logarithmic Sobolev inequality,generalized Cheeger isoperimetric inequality,transportation-information inequality and transportation-entropy inequality) for reversible nearest-neighbor Markov processes on connected finite graphs by means of(random) path method.We provide estimates of the involved constants.     

常曲率平面上的逆Bonnesen型不等式

利用积分几何中估计包含测度的思想给出常曲率平面上一些新的逆Bonnesen型不等式.这些不等式在欧氏平面上为著名的Bottema不等式的改进形式与新的逆Bonnesen型不等式.