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A Reverse Hardy-Hilbert-Type Inequality

Abstract

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.

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References

  1. 1.

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

    Google Scholar 

  2. 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)00129-9

    MathSciNet  Article  MATH  Google Scholar 

  3. 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.1999.6295

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Yang B: On a strengthened version of the more precise Hardy-Hilbert inequality. Acta Mathematica Sinica. Chinese Series 1999,42(6):1103–1110.

    MathSciNet  MATH  Google Scholar 

  5. 5.

    Yang B, Rassias TM: On a new extension of Hilbert's inequality. Mathematical Inequalities & Applications 2005,8(4):575–582.

    MathSciNet  Article  MATH  Google Scholar 

  6. 6.

    Yang B: On a new extension of Hilbert's inequality with some parameters. Acta Mathematica Hungarica 2005,108(4):337–350. 10.1007/s10474-005-0229-4

    MathSciNet  Article  MATH  Google Scholar 

  7. 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. 8.

    Wang Z, Dunren G: An Introduction to Special Function. Science Press, Beijing, China; 1979.

    Google Scholar 

  9. 9.

    Kuang J: Applied Inequalities. Sandong Science and Technology Press, Jinan, China; 2004.

    Google Scholar 

Download references

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Correspondence to Gaowen Xi.

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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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Xi, G. A Reverse Hardy-Hilbert-Type Inequality. J Inequal Appl 2007, 079758 (2007). https://doi.org/10.1155/2007/79758

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Keywords

  • Weight Coefficient
  • Equivalent Form
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