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.     

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.     

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。     

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.     

拟凸函数和Hadamard不等式

建立了若干关于拟凸函数的新的Hadamard型不等式,所得结果包含了某些文献中的结果作为我们不等式的特例.     

关于n个独立变元的欧阳型非线性积分不等式

讨论R^n上的Ou-Iang型非线性积分不等式，所得结论是杨恩浩的R^1上的Ou-Iang型非线性积分不等式的自然推广和改进。     

On some dynamic inequalities of Steffensen type on time scales

In the present article, we investigate some new inequalities of Steffensen type on an arbitrary time scale using the diamond‐α dynamic integrals, which are defined as a linear combination of the delta and nabla integrals. The obtained inequalities extend some known dynamic inequalities on time scales and unify and extend some continuous inequalities and their discrete analogues.     

Half-linear Volterra-Fredholm type integral inequalities on time scales and their applications

The main aim of this paper is to establish some new half-linear Volterra-Fredholm type integral inequalities on time scales. Our results not only extend and complement some known integral inequalities but also provide an effective tool for the study of qualitative properties of solutions of some dynamic equations.     

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．     

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。     

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.     

Some quantum estimates of Hermite-Hadamard inequalities for convex functions

In this study, based on a new quantum integral identity, we establish some quantum estimates of Hermite-Hadamard type inequalities for convex functions. These results generalize and improve some known results given in literatures.     

On a mixed Kernel Hilbert‐type integral inequality and its operator expressions with norm

By using some real analysis techniques, we study the structural characteristics of a multi‐parameter Hilbert‐type integral inequality with the hybrid kernel and obtain some equivalent conditions for this inequality. We also consider the operator expression of the equivalent inequalities. The conclusions not only integrate some results of references but also find some new Hilbert‐type integral inequalities with simple form by choosing suitable parameter values.     

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.     

A Cotlar type inequality for the multilinear singular integral operators and its applications

A Cotlar type inequality is established for the multilinear singular integral operators. As applications, some two-weight norm inequalities are obtained for the maximal operator corresponding to the multilinear singular integral operators.     

Some new explicit bounds for weakly singular integral inequalities with applications to fractional differential and integral equations

Some new weakly singular integral inequalities of Gronwall-Bellman type are established, which generalized some known weakly singular inequalities and can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. Some applications to fractional differential and integral equations are also indicated.     

逆向型Hilbert-Pachpatte不等式

建立了逆向型Hilbert-Pachpatte不等式,推广和改进了离散型和连续型Pach- patte不等式的逆.     

两个严格的加权Ostrowski型不等式

使用Cauchy积分不等式和Grüss不等式的变式得到两个严格的加权Ostrowski型不等式.     

关于区间Katugampola分数阶积分的若干Hermite-Hadamard型不等式

主要引入了区间值函数Katugampola分数阶积分的概念.利用区间分析及区间凸函数理论,得到了区间Katugampola分数阶积分Hermite-Hadamard型不等式.     

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。