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A Hilbert inequality and an Euler-Maclaurin summation formula

Published online by Cambridge University Press:  17 February 2009

Mario Krnić  and
Josip Pečarić
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Abstract

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We obtain a generalized discrete Hilbert and Hardy-Hilbert inequality with non-conjugate parameters by means of an Euler-Maclaurin summation formula. We derive some general results for homogeneous functions and compare our findings with existing results. We improve some earlier results and apply the results to some special homogeneous functions.

Keywords

inequalitiesHilbert's inequalityBernoulli numbersBernoulli polynomialsEuler-Maclaurin summation formulahomogeneous functionkernelweight functionequivalent inequalities.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 3 , January 2007 , pp. 419 - 431
Copyright
Copyright © Australian Mathematical Society 2007

References

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