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New Inequalities Similar to Hardy-Hilbert Inequality and their Applications

Journal of Inequalities and Applications volume 2007, Article number: 090641 (2008) Cite this article

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.

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References

  1. Hardy GH, Littlewood JE, Pólya G: Inequalities. 2nd edition. Cambridge University Press, London, UK; 1952:xii+324.

    MATH  Google 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.1997.5490

    Article  MathSciNet  MATH  Google Scholar 

  3. Yang B: Some generalizations of the Hardy-Hilbert integral inequalities. Acta Mathematica Sinica 1998,41(4):839–844.

    MathSciNet  MATH  Google Scholar 

  4. Yang B: On Hilbert's integral inequality. Journal of Mathematical Analysis and Applications 1998,220(2):778–785. 10.1006/jmaa.1997.5877

    Article  MathSciNet  MATH  Google 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.2000.6766

    Article  MathSciNet  Google 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.1999.6373

    Article  MathSciNet  MATH  Google 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.2000.6766

    Article  MathSciNet  MATH  Google 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.

    Article  MathSciNet  MATH  Google Scholar 

  10. Yang B: On a new inequality similar to Hardy-Hilbert's inequality. Mathematical Inequalities & Applications 2003,6(1):37–44.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Xuzhou Normal University, Xuzhou, Jiangsu, 221116, China

    Lü Zhongxue

  2. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China

    Xie Hongzheng

Authors
  1. Lü Zhongxue
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  2. Xie Hongzheng
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Correspondence to Lü Zhongxue.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Zhongxue, L., Hongzheng, X. New Inequalities Similar to Hardy-Hilbert Inequality and their Applications. J Inequal Appl 2007, 090641 (2008). https://doi.org/10.1155/2007/90641

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  • DOI: https://doi.org/10.1155/2007/90641

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