New Inequalities Similar to Hardy-Hilbert Inequality and their Applications

Lü Zhongxue; Xie Hongzheng

doi:10.1155/2007/90641

Research Article
Open Access

New Inequalities Similar to Hardy-Hilbert Inequality and their Applications

Lü Zhongxue¹Email author and
Xie Hongzheng²

Journal of Inequalities and Applications20082007:090641

https://doi.org/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.

Keywords

Real Function

[12345678910]

Authors’ Affiliations

(1)

School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, China

(2)

Department of Mathematics, Harbin Institute of Technology, Harbin, China

References

Hardy GH, Littlewood JE, Pólya G: Inequalities. 2nd edition. Cambridge University Press, London, UK; 1952:xii+324.MATHGoogle Scholar
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
Yang B: Some generalizations of the Hardy-Hilbert integral inequalities. Acta Mathematica Sinica 1998,41(4):839–844.MathSciNetMATHGoogle Scholar
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
Yang B: A generalized Hilbert's integral inequality with the best const. Chinese Annals of Mathematics 2000,21A(4):401–408.Google Scholar
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
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
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
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
Yang B: On a new inequality similar to Hardy-Hilbert's inequality. Mathematical Inequalities & Applications 2003,6(1):37–44.MathSciNetView ArticleMATHGoogle Scholar

Copyright

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.