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A Multiple Hilbert-Type Integral Inequality with the Best Constant Factor

Abstract

By introducing the norm and two parameters,, we give a multiple Hilbert-type integral inequality with a best possible constant factor. Also its equivalent form is considered.

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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.

    Mitrinović DS, Pečarić JE, Fink AM: Inequalities Involving Functions and Their Integrals and Derivatives, Mathematics and Its Applications (East European Series). Volume 53. Kluwer Academic Publishers, Dordrecht, The Netherlands; 1991:xvi+587.

    Google Scholar 

  3. 3.

    Gao M, Yang B: On the extended Hilbert's inequality. Proceedings of the American Mathematical Society 1998,126(3):751–759. 10.1090/S0002-9939-98-04444-X

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Jichang K, 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

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Jichang K: Applied Inequalities. Shandong Science and Technology Press, Jinan, China; 2004.

    Google Scholar 

  6. 6.

    Pachpatte BG: On some new inequalities similar to Hilbert's inequality. Journal of Mathematical Analysis and Applications 1998,226(1):166–179. 10.1006/jmaa.1998.6043

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Yang B, Debnath L: On new strengthened Hardy-Hilbert's inequality. International Journal of Mathematics and Mathematical Sciences 1998,21(2):403–408. 10.1155/S0161171298000556

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Yang B: On a general Hardy-Hilbert's integral inequality with a best constant. Chinese Annals of Mathematics. Series A 2000,21(4):401–408.

    MathSciNet  MATH  Google Scholar 

  9. 9.

    Yang B: On a generalization of a Hilbert's type integral inequality and its applications. Mathematica Applicata 2003,16(2):82–86.

    MathSciNet  MATH  Google Scholar 

  10. 10.

    Hong Y: All-sided generalization about Hardy-Hilbert integral inequalities. Acta Mathematica Sinica. Chinese Series 2001,44(4):619–626.

    MathSciNet  MATH  Google Scholar 

  11. 11.

    Yang B: A multiple Hardy-Hilbert integral inequality. Chinese Annals of Mathematics. Series A 2003,24(6):743–750.

    MathSciNet  MATH  Google Scholar 

  12. 12.

    Yong H: A multiple Hardy-Hilbert integral inequality with the best constant factor. Journal of Inequalities in Pure and Applied Mathematics 2006,7(4, article 139):10.

    MathSciNet  Google Scholar 

  13. 13.

    Hua L: An Introduction to Advanced Mathematics (Remaining Sections). Science Publishers, Beijing, China; 1984.

    Google Scholar 

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Correspondence to Baoju Sun.

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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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Sun, B. A Multiple Hilbert-Type Integral Inequality with the Best Constant Factor. J Inequal Appl 2007, 071049 (2007). https://doi.org/10.1155/2007/71049

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Keywords

  • Constant Factor
  • Equivalent Form
  • Integral Inequality
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