Grüss-Type Inequalities

A connection between Grüss inequality and the error of best approximation is revealed. A Grüss-type inequality that unifies the continuous and discrete versions of the classical Grüss inequalities is established.     

On Grüss Type Inequalities for Double Integrals

We establish two new inequalities of Grüss type involving functions of two independent variables. The analysis used in the proofs is elementary and our results provide new estimates on inequalities of this type.     

Translation-invariant maps and applications

In this paper we study translation-invariant maps on a linear space. A method for estimating quantities induced by such maps is presented. Applications for differences of operators, commutators, G-contractive maps and Grüss type inequalities are also given.     

Grüss type inequalities in inner product modules

In this paper we give some properties of a generalized inner product in modules over H*-algebras and C*-algebras and we obtain inequalities of Grüss type.

     

半序线性空间上线性泛函的两个Gr\"{u}ss型不等式$^{}$

证明了半序线性空间上线性泛函的两个Gr\"{u}ss型不等式, 并由此给出了Karamata型积分不等式的一种推广形式, 得到了一个新的Gr\"{u}ss型积分不等式及关于傅立叶系数的两个不等式. 最后利用所得结论研究了关于矩阵及线性算子的一些Gr\"{u}ss型不等式.     

Another Grüss Type Inequality for Sequences of Vectors in Normed Linear Spaces and Applications

A discrete inequality of Grüss type in normed linear spaces and applications for the Fourier transform, Mellin transform of sequences, for polynomials with coefficients in normed spaces and for vector valued Lipschitzian mappings, are given.     

On first order interpolation inequalities with weights on the Heisenberg group

In this paper, sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg group are given. The necessity is discussed by polar coordinates changes of the Heisenberg group. Establishing a class of Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation, we derive the sufficiency. Finally, sharp constants for Hardy type inequalities are determined.     

A Grüss Type Discrete Inequality in Inner Product Spaces and Applications

A Grüss type inequality in inner product spaces and applications for the discrete Fourier transform, Mellin transform of sequences, polynomials with coefficients in Hilbert spaces, and Lipschitzian vector valued mappings are given.     

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．     

Moment inequalities for the partial sums of random variables

This paper discusses the conditions under which Rosenthal type inequality is obtained from M-Z-B type inequality. And M-Z-B type inequality is proved for a wide class of random variables. Hence Rosenthal type inequalities for some classes of random variables are obtained.     

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。     

Nonlinear discrete inequalities with two variables and their applications

An error in the proof of Theorem 1 by Zheng et al. [K. Zheng, Y. Wu, S. Zhong, Discrete nonlinear integral inequalities in two variables and their applications, Appl. Math. Comput. 207 (2009) 140-147] is reported. This paper gives the right proof under some additional condition. Application examples to show boundedness and uniqueness of solutions of a Volterra type difference equation are also given.     

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.     

Grüss type and related integral inequalities in probability spaces

Aequationes mathematicae - In this paper we study Grüss type inequalities for real and complex valued functions in probability spaces. Some earlier Grüss type inequalities are extended...     

Plancherel-Pôlya type inequality on spaces of homogeneous type and its applications

In this paper, using the discrete Calderon reproducing formula on spaces of homogeneous type obtained by the author, we obtain the Plancherel-Pôlya type inequalities on spaces of homogeneous type. These inequalities give new characterizations of the Besov spaces and the Triebel-Lizorkin spaces on spaces of homogeneous type introduced earlier by the author and E. T. Sawyer and also allow us to generalize these spaces to the case where . Moreover, using these inequalities, we can easily show that the Littlewood-Paley -function and -function are equivalent on spaces of homogeneous type, which gives a new characterization of the Hardy spaces on spaces of homogeneous type introduced by Macias and Segovia.

     

Two-weight norm inequalities for commutators of potential type integral operators

We give a condition which is sufficient for the two-weight (p,q) inequalities for commutators of potential type integral operators.     

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．     

一个较为精密的Hardy-Hilbert型不等式及其应用

利用改进的Euler-Maclaurin求和公式,求出一个较为精密的Hardy-Hilbert 型不等式．作为应用,给出它的等价形式及一些特殊结果．本文的引理及定理对研究这一类不等式提供了一些新的估算方法．     

Multivariate inequalities based on Sobolev representations

Here we derive very general multivariate tight integral inequalities of Chebyshev–Grüss, Ostrowski types and of comparison of integral means. These are based on well-known Sobolev integral representation of a function. Our inequalities engage ordinary and weak partial derivatives of the involved functions. We also give their applications. On the way to prove our main results we derive important estimates for the averaged Taylor polynomials and remainders of Sobolev integral representations. Our results expand to all possible directions.