On Some Generalizations  of the Hilbert -Hardy Type Integral Inequalities

S A  A  El Marouf

doi:10.17485/ijst/2013/v6i2.6

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On Some Generalizations of the Hilbert -Hardy Type Integral Inequalities

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2013/v6i2.6

Year: 2013, Volume: 6, Issue: 2, Pages: 1-14

Original Article

On Some Generalizations of the Hilbert -Hardy Type Integral Inequalities

S A. A .El-Marouf

Department of Mathematics, Faculty of Science, Minoufiya University,
Department of Mathematics, Faculty of Science,Taibah University, [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

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. 2010 Mathematical Subject Classification: 26D15.
Keywords:Hilbert's inequality, Hölder's inequality, Hardy's inequality, Beta and Gamma functions, Weight functions.