International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2004 / Article

Open Access

Volume 2004 |Article ID 861720 | https://doi.org/10.1155/S0161171204205270

Lü Zhongxue, "On further strengthened Hardy-Hilbert's inequality", International Journal of Mathematics and Mathematical Sciences, vol. 2004, Article ID 861720, 5 pages, 2004. https://doi.org/10.1155/S0161171204205270

On further strengthened Hardy-Hilbert's inequality

Received07 May 2002

Abstract

We obtain an inequality for the weight coefficient ω(q,n) (q>1, 1/q+1/q=1, n) in the form ω(q,n)=:m=1(1/(m+n))(n/m)1/q<π/sin(π/p)1/(2n1/p+(2/a)n1/q) where 0<a<147/45, as n3; 0<a<(1C)/(2C1), as n=1,2, and C is an Euler constant. We show a generalization and improvement of Hilbert's inequalities. The results of the paper by Yang and Debnath are improved.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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