On the Hilbert Type Integral Inequalities with Some Parameters and Its Reverse (original) (raw)

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

Mathematical Inequalities & Applications, 2008

By introducing some parameters and a norm |x| α , x ∈ R + n , 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.

New Hilbert–Pachpatte Type Integral Inequalities

Journal of Mathematical Analysis and Applications, 2001

In this paper we obtain a new class of multivariable integral inequalities of Hilbert type. By specializing the upper estimate functions in the hypothesis and the parameters, we obtain many special cases, which include, in particular, the integral inequalities derived recently by Pachpatte.

New Inequalities of Hardy-Hilbert Type

2010

In this paper, we establish a new inequality of Hardy-Hilbert type. As applications, some particular results and an equivalent form are derived. The integral analogues of the main results are also given. Mathematics subject classification: 26D15.

New inequalities similar to Hardy-Hilbert's inequality

2010

In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.

General Hilbert's and Hardy's inequalities

Mathematical Inequalities & Applications, 2005

In this paper we make some further generalizations of well known Hilbert's inequality and its equivalent form in two dimensional case. We also derive some results on Hardy's inequality. Then we apply our general results to homogeneous functions. A reverses of Hilbert's inequality are also given in integral case. Many other results of this type in recent years, follows as a special case of our results.

Some new refined Hardy type integral inequalities

arXiv: Classical Analysis and ODEs, 2015

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

Hilbert-Type Inequalities Revisited

Journal of Mathematics and Statistics, 2016

Considering different parameters, Hilbert-type integral inequality for functions f(x), g(x) in L 2 [0, ∞) will be generalized.

On Some Fractional Hardy-Hilbert’s Integral Inequalities

General Letters in Mathematics, 2019

We focus our attention in this article on some recent results regarding Hardy-Hilbert's inequalities. We derive an equivalent form using katugampola Fractional Calculus and introduce new analogs to some Hardy-Hilbert's type inequality. Several special cases are also given.