Hilbert's Integral Inequality Research Articles

Some Lower Bounds for a Double Integral Depending on Six Adaptable Functions

This paper is devoted to sharp lower bounds of a special double integral depending on six adaptable functions. The bounds obtained depend on simple integrals. Some connections with the famous Hilbert integral inequality and its variants are made. Several numerical examples illustrate the results.

On a New Inequality Similar to the Hardy - Hilbert Integral Inequality

On a New Inequality Similar to the Hardy - Hilbert Integral Inequality

New analogues of Hilbert integral inequality of three variables

New analogues of Hilbert integral inequality of three variables

A new form of Hilbert integral inequality

In this paper we obtain two new forms of the Hilbert inequality. The first form is a sharper form of the classical Hilbert inequality and is connected to Hardy inequality. In the second one we introduce a differential form of Hilbert inequality. Mathematics subject classification (2010): 26D15.

Reverse Hilbert's type integral inequalities

In this paper, we are motivated by some newer Hilbert-Pachpatte inequalities, and that we derive some similar (but reverse) inequalities. Mathematics subject classification (2010): 26D15.

Two new forms of Hilbert integral inequality

Two new forms of Hilbert integral inequality

The connection between Hilbert and Hardy inequalities

In this paper we introduce some new forms of the Hilbert integral inequality, and we study the connection between the obtained inequalities with Hardy inequalities. The reverse form and some applications are also given. MSC:26D15.

On Some Generalizations of the Hilbert-Hardy Type Integral Inequalities

In this paper, new generalization of Hilbert's integral inequality is presented by using new techniques in proof. By the weight coefficient functions in the hypothesis and the parameters, we obtained many special cases which include, in particular, the integral inequalities derived by Hilbert, Hardy and Salem. As an application of our results, we construct some examples that ensure our results.

A Hilbert integral inequality with Hurwitz zeta function

They are the famous Hilbert integral inequalities, where the constant factors π2 and π are the best possible. And the equalities in (1.1) and (1.2) hold if and only if f (x) = 0, or g(x) = 0. These results can be found in papers [1] and [2]. Owing to the importance of the Hilbert inequality and the Hilbert type inequality in Mathematical analysis and applications, some mathematicians have been studying them. Recently, various refinements, extensions and generalizations of (1.2) appear in a great deal of the articles (such as [3]–[10] etc.). However, the research articles of (1.1) are few. The aim of the present paper is to build an inequality of the form

On Hilbert's integral inequality and its applications

In this paper it is shown that a new improvement on Hilbert's integral inequality can be established by introducing a weight function of the form 1 1+ √ x − 1 1+x (with x 0) .A s

Some extensions of Hilbert's integral inequality

(Communicated by I. Franjic) Abstract. In this paper we introduce a new extension of Hilbert's integral inequality with a best constant factor involving the hypergeometric function. The equivalent form and some examples will be given.

On a Hilbert-Type Integral Inequality with a Combination Kernel and Applications

By introducing some parameters and using the way of weight function and the technic of real analysis and complex analysis, a new Hilbert-type integral inequality with a best constant factor and a combination kernel involving two mean values is given, which is an extension of Hilbert's integral inequality. As applications, the equivalent form and the reverse forms are considered.

On a Relation to Hilbert's Integral Inequality and a Hilbert-Type Inequality

In this paper, by introducing some parameters and using the way of weight function, a new integral inequality with a best constant factor is given, which is a relation between Hilbert's integral inequality and a Hilbert-type inequality. As applications, the equivalent form, the reverse forms and some particular inequalities are considered.

An Extension of the Hilbert's Integral Inequality

It is shown that an extension of the Hilbert's integral inequality can be established by introducing two parameters and . The constant factors expressed by the Euler number and as well as by the Bernoulli number and , respectively, are proved to be the best possible. Some important and especial results are enumerated. As applications, some equivalent forms are given.

On Certain Extension of Hilbert's Integral Inequality with Best Constants

In this paper, by introducing a new function with two parameters, we give another generalizations of the Hilbert's integral inequality with a mixed kernel k(x,y) = 1 A(x+y)+B|x y| and a best constant factors. As applications, some particular results with the best constant factors are considered.

On New Extensions of Hilbert's Integral Inequality

It is shown that some new extensions of Hilbert's integral inequality with parameterλ(λ>1/2)can be established by introducing a proper weight function. In particular, whenλ=1, a refinement of Hilbert's integral inequality is obtained. As applications, some new extensions of Widder's inequality and Hardy-Littlewood's inequality are given.

On some higher-dimensional Hilbert's and Hardy-Hilbert's integral inequalities with parameters

By introducing some parameters and a norm |x|α , x ∈ R+ , we give higherdimensional Hilbert’s and Hardy-Hilbert’s integral inequalities in non-conjugate case. Further, we prove that their constant factors are the best possible, in the conjugate case, when the parameters satisfy appropriate conditions. We also compare our results with some known results. Mathematics subject classification (2000): 26D15.

On a New Weighted Hilbert Inequality

It is shown that a weighted Hilbert inequality for double series can be established by introducing a proper weight function. Thus, a quite sharp result of the classical Hilbert inequality for double series is obtained. And a similar result for the Hilbert integral inequality is also proved. Some applications are considered.

Hilbert's Type Linear Operator and Some Extensions of Hilbert's Inequality

The norm of a Hilbert's type linear operator is given. As applications, a new generalizations of Hilbert integral inequality, and the result of series analogues are given correspondingly.

An extension on the Hardy-Hilbert integral inequality and its applications

In this article, it is shown that some new extensions on the Hardy-Hilbert inequality related to exponent function can be established by introducing a parameter λ (1 − q 1) and two exponent functions Aa x (A > 0,a > 1) and Bb y (B > 0,b > 1). In particular, for the case p = 2, an extension of the Hilbert integral inequality is built. As an application, a new Hardy-Littlewood integral inequality is given.