Open Access

A Reverse Hardy-Hilbert-Type Inequality

Journal of Inequalities and Applications20072007:079758

DOI: 10.1155/2007/79758

Received: 12 December 2006

Accepted: 12 March 2007

Published: 19 April 2007


By estimating the weight coefficient, a reverse Hardy-Hilbert-type inequality is proved. As applications, some equivalent forms and a number of particular cases are obtained.


Authors’ Affiliations

Department of Mathematics, Luoyang Teachers' College


  1. Hardy GH, Littlewood JE, Pólya G: Inequalities. 2nd edition. Cambridge University Press, Cambridge, UK; 1952:xii+324.MATHGoogle Scholar
  2. Yang B, Debnath L: Some inequalities involvingand an application to Hilbert's inequality. Applied Mathematics Letters 1999,12(8):101–105. 10.1016/S0893-9659(99)00129-9MathSciNetView ArticleMATHGoogle Scholar
  3. Yang B, Debnath L: On a new generalization of Hardy-Hilbert's inequality and its applications. Journal of Mathematical Analysis and Applications 1999,233(2):484–497. 10.1006/jmaa.1999.6295MathSciNetView ArticleMATHGoogle Scholar
  4. Yang B: On a strengthened version of the more precise Hardy-Hilbert inequality. Acta Mathematica Sinica. Chinese Series 1999,42(6):1103–1110.MathSciNetMATHGoogle Scholar
  5. Yang B, Rassias TM: On a new extension of Hilbert's inequality. Mathematical Inequalities & Applications 2005,8(4):575–582.MathSciNetView ArticleMATHGoogle Scholar
  6. Yang B: On a new extension of Hilbert's inequality with some parameters. Acta Mathematica Hungarica 2005,108(4):337–350. 10.1007/s10474-005-0229-4MathSciNetView ArticleMATHGoogle Scholar
  7. Yang B: A reverse of the Hardy-Hilbert's type inequality. Journal of Southwest China Normal University (Natural Science) 2005,30(6):1012–1015.Google Scholar
  8. Wang Z, Dunren G: An Introduction to Special Function. Science Press, Beijing, China; 1979.Google Scholar
  9. Kuang J: Applied Inequalities. Sandong Science and Technology Press, Jinan, China; 2004.Google Scholar


© Gaowen Xi 2007

This article is published under license to BioMed Central Ltd. 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.