Open Access

New Inequalities Similar to Hardy-Hilbert Inequality and their Applications

Journal of Inequalities and Applications20082007:090641

DOI: 10.1155/2007/90641

Received: 25 January 2007

Accepted: 22 November 2007

Published: 6 February 2008

Abstract

Two classes of new inequalities similar to Hardy-Hilbert inequality are showed by introducing some parameters and two real functions and . Some applications are obtained.

[12345678910]

Authors’ Affiliations

(1)
School of Mathematical Sciences, Xuzhou Normal University
(2)
Department of Mathematics, Harbin Institute of Technology

References

  1. Hardy GH, Littlewood JE, Pólya G: Inequalities. 2nd edition. Cambridge University Press, London, UK; 1952:xii+324.MATHGoogle Scholar
  2. Gao M: On Hilbert's inequality and its applications. Journal of Mathematical Analysis and Applications 1997,212(1):316–323. 10.1006/jmaa.1997.5490MathSciNetView ArticleMATHGoogle Scholar
  3. Yang B: Some generalizations of the Hardy-Hilbert integral inequalities. Acta Mathematica Sinica 1998,41(4):839–844.MathSciNetMATHGoogle Scholar
  4. Yang B: On Hilbert's integral inequality. Journal of Mathematical Analysis and Applications 1998,220(2):778–785. 10.1006/jmaa.1997.5877MathSciNetView ArticleMATHGoogle Scholar
  5. Yang B: A generalized Hilbert's integral inequality with the best const. Chinese Annals of Mathematics 2000,21A(4):401–408.Google Scholar
  6. Yang B, Debnath L: On a new generalization of Hardy-Hilbert's inequality and its applications. Journal of Mathematical Analysis and Applications 2000,245(1):248–265. 10.1006/jmaa.2000.6766MathSciNetView ArticleGoogle Scholar
  7. Kuang J: Note on new extensions of Hilbert's integral inequality. Journal of Mathematical Analysis and Applications 1999,235(2):608–614. 10.1006/jmaa.1999.6373MathSciNetView ArticleMATHGoogle Scholar
  8. Kuang J, Debnath L: On new generalizations of Hilbert's inequality and their applications. Journal of Mathematical Analysis and Applications 2000,245(1):248–265. 10.1006/jmaa.2000.6766MathSciNetView ArticleMATHGoogle Scholar
  9. Yang B, Rassias TM: On the way of weight coefficient and research for the Hilbert-type inequalities. Mathematical Inequalities & Applications 2003,6(4):625–658.MathSciNetView ArticleMATHGoogle Scholar
  10. Yang B: On a new inequality similar to Hardy-Hilbert's inequality. Mathematical Inequalities & Applications 2003,6(1):37–44.MathSciNetView ArticleMATHGoogle Scholar

Copyright

© L. Zhongxue and X. Hongzheng 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.