DOI QR코드

DOI QR Code

Generalization of Hardy-Hilbert's Inequality and Applications

  • Saglam, Aziz ;
  • Yildirim, Huseyin ;
  • Sarikaya, Mehmet Zeki
  • Received : 2009.03.25
  • Accepted : 2009.07.09
  • Published : 2010.03.31

Abstract

In this paper, by introducing some parameters we establish an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series. As an application, the reverses, some particular results and their equivalent forms are considered.

Keywords

Hardy-Hilbert-type integral inequality;H$\"{o}$older's inequality

References

  1. L. E. Azar, On Some Extensions of Hardy-Hilbert's Inequality and Applications, Journal of Inequalities and Applications, 2008(2008), Article ID 546829, 14 pages.
  2. G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, London, UK, 2nd edition, 1952.
  3. G. H. Hardy, Note on a theorem of Hilbert concerning series of positive terms, Proceedings of the London Mathematical Society, 23(2)(1925), 45-46. https://doi.org/10.1112/plms/s2-23.1.45
  4. Y. Li, Z. Wang, and B. He, Hilbert's type linear operator and some extensions of Hilbert's inequality, Journal of Inequalities and Applications, 2007(2007), Article ID 82138, 10 pages.
  5. D. S Mitrinovic, J. E. Pecaric and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, vol. 53 of Mathematics and Its Applications, Kluwer Academic Publishers, The Netherlands, 1991.
  6. B. Yang, On an extension of Hilbert's integral inequality with some parameters, The Australian Journal of Mathematical Analysis and Applications, 1(1)(2004), article 11, 1-8.
  7. B. Yang, On the extended Hilbert's integral inequality, Journal of Inequalities in Pure Applied Mathematics, 5(4)(2004), article 96, 1-8.
  8. B. Yang, Generalization of a Hilbert type inequality and its applications, Chinese Journal of Engineering Mathematics, 21(5)(2004), 821-824.
  9. B. Yang, On a Hilbert-type operator with a synnetric homogeneous Kernel of 1-order and applications, Journal of Inequalities and Applications, 2007(2007), Article ID 47812, 9 pages.
  10. G. Xi, A reverse Hardy-Hilbert-type inequality, Journal of Inequalities and Applications, 2007(2007), Article ID 79758, 7 pages.