关于Hermite-Hadamard积分不等式的推广（英文）

Some new inequalities of Hermite-Hadamard's integration are established. As for as inequalities about the righthand side of the classical Hermite-Hadamard's integral inequality refined by S Qaisar in [3], a new upper bound is given. Under special conditions,the bound is smaller than that in [3].     

关于s-凸函数的Hermite-Hadamard型积分不等式的推广（英文）

Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.     

Some inequalities of Hermite-Hadamard type for s-convex functions

In this paper several inequalities of the left-hand side of Hermite-Hadamard’s inequality are obtained for s-convex functions.     

涉及广义积分及其离散模型的某些非线性不等式

§ 1　IntroductionAs well-known thatthe theory of Gronwall-Bellman type integral inequalities,both inone and more than one variable,is crucial and indispensable in the development of almostall kinds of analytic equations such as differential and integral equations,integro-differen-tial equations,functional-differential equations and evolution equations.However,only afew investigation works appreared so far in the literature which dealt with Gronwall typeinequalities involving improper integra…     

On new generalizations of the Hilbert integral inequality

Some new generalizations of the Hilbert integral inequality by introducing real functions ?(x) and ψ(x). The results of this paper reduce to those of the corresponding inequalities proved by Gao [Mingzhe Gao, On Hilbert's integral inequality, Math. Appl. 11 (3) (1998) 32-35]. Some applications are considered.     

关于两个新Hilbert积分不等式

利用分析的方法及不等式理论，推广了Pachpatte最新给出的两个新型Hilbert积分不等式，获得了几个新结果，改进了某些相关的结果。     

Aczel积分形的不等式推广

在文献［１］推广了有限和式的Ａｃｚｅｌ不等式，本文继续给出积分形式的Ａｃｚｅｌ不等式。     

关于新型Hilbert不等式的积分形式

本文利用分析的方法及不等式理论，建立了两个新型Hilbert不等式的积分形式，获得了一些新结果，推广了某些相关的结果．     

一些Pachpatte不等式的加强与反向形式

本文建立了一些新的加强和反向Pachpatte不等式.作为应用,推广和加强了一些新型Hilbert不等式.     

弱奇性Volterra积分不等式解的估计

Medved对弱奇性Gronwall型和Henry型积分不等式解的估计提出一种新方法，本文将他的方法稍加改进用来研究更广的Volterra型弱奇性线笥及非线性积分不等式解的估计，导出解的先验逐点界公式，并举例说明了结果的应用。     

离散和连续型Pachpatte不等式的逆

本文利用分析的方法和不等式理论,建立了离散型和连续型Pachpatte不等 式的逆向不等式.作为应用,推广并改进了一些新型Hilbert不等式.     

关于未解决的一个不等式问题的注记(英文)

文[6]中,F.Qi提出了一个未解决的不等式问题.本文给出了此问题的答案和进一步的拓广,同时也得到了该问题的反向不等式.     

Hardy-Hilbert积分不等式的全方位推广

本文对 Ｈａｒｄｙ－Ｈｉｌｂｅｒｔ积分不等式进行了积分重数和多参数方面的全方位推广,同时得到了很多形式优美的全新不等式．     

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。     

Some new Gronwall-Bellman-Bihari type integral inequalities with delay

Some new linear and nonlinear delay integral inequalities of G-B-B type are obtained which generalize some results of O. Akinyele [1], P. Ch. Tsamatos and S. K. Ntouyas [16]. Application examples are also given. This revised version was published online in June 2006 with corrections to the Cover Date.     

On some nonlinear integral and discrete inequalitites related to Ou-Iang's inequality

Nonlinear integral and discrete inequalities are obtained, which are related to some recent results of B. G. Pachpatte in [1] given therein as generalizations of Ou-Iang's integral inequality [2]. As special cases, some new inequalities with the power nonlinearity are derived from the main results. To show the contribution of our results, boundedness of solutions to certain nonlinear difference equation is also considered. The project is supported in part by the NSF of Guangdong Province (Grnat No. 940651) and the SF of Key Discipline of the State Council Office of Overseas Chinese Affairs of China (Grant No. 93-93-6).     

Simpson and Newton type inequalities for convex functions via newly defined quantum integrals

We first establish two new identities, based on the kernel functions with either two section or three sections, involving quantum integrals by using new definition of quantum derivative. Then, some new inequalities related to Simpson's 1/3 formula for convex mappings are provided. In addition, Newton type inequalities, for functions whose quantum derivatives in modulus or their powers are convex, are deduced. We also mention that the results in this work generalize inequalities given in earlier study.     

Lebesgue-stieltjes integral inequalities in several variables with retardation

The aim of this paper is to establish some new Lebesgue-Stieltjes integral inequalities inn independent variables with retardation which generalize and unify continuous and discrete inequalities of the Gronwall-Bellman-Bihari type inn independent variables.     

Rearrangement Free Method for Hardy-Littlewood-Sobolev Inequalities on $\mathbb{S}^n$

For conformal Hardy-Littlewood-Sobolev(HLS) inequalities [22] and reversed conformal HLS inequalities [8] on $\mathbb{S}^n,$ a new proof is given for the attainability of their sharp constants. Classical methods used in [22] and [8] depends on rearrangement inequalities. Here, we use the subcritical approach to construct the extremal sequence and circumvent the blow-up phenomenon by renormalization method. The merit of the method is that it does not rely on rearrangement inequalities.     

Some inequalities of Qi type for double integrals

In the paper, the authors establish some new inequalities of Qi type for double integrals on a rectangle, from which some known integral inequalities of Qi type may be derived.