On some new variations of Hardy type inequalities

Volume 10, Issue 4, pp 1709--1713 http://dx.doi.org/10.22436/jnsa.010.04.33

Publication Date: April 20, 2017 Submission Date: January 01, 2017

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Authors

Zareen A. Khan - Department of Mathematics, Princess Nora Bint Abdul Rahman University, Riyadh, KSA.

Abstract

The goal of this paper is to establish some new variations of the inequalities which originate from the well-known Hardy type inequalities. The method applied in this paper to achieve our results is related to the idea used by Levinson to obtain the generalizations of Hardy’s integral inequality.

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Keywords

• Hardy type inequality
• Hölder’s inequality.

MSC

•  426D15

References

• [1] G. H. Hardy, Note on a theorem of Hilbert, Math. Z., 6 (1920), 314–317.
  • View Article
  • MathSciNet
  • Google Scholar


• [2] G. H. Hardy, J. E. Littlewood, G. Pólya , Inequalities, 2d ed., Cambridge, at the University Press (1952)
  • Google Scholar


• [3] M. Izumi, S.-I. Izumi, On some inequalities for Fourier series, J. Analyse Math., 21 (1968), 277–291.
  • View Article
  • MathSciNet
  • Google Scholar


• [4] N. Levinson, Generalizations of an inequality of Hardy, Duke Math. J., 31 (1964), 389–394.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] D. S. Mitronović, Analytic Inequalities, In cooperation with P. M. Vasić, Die Grundlehren der mathematischen Wissenschaften, Band 165 Springer-Verlag, New York-Berlin (1970)
  • View Article
  • Google Scholar


• [6] B. G. Pachpatte, On a new class of Hardy type inequalities, Proc. Roy. Soc. Edinburgh Sect. A, 105 (1987), 265–274.
  • View Article
  • Google Scholar


• [7] S. Salem, On some integral inequalities of Hardy type, Kyungpook Math. J., 35 (1995), 193–203.
  • Google Scholar


• [8] M. Z. Sarikaya, H. Yildirim, Some Hardy type integral inequalities, JIPAM. J. Inequal. Pure Appl. Math., 7 (2006), 5 pages.
  • Google Scholar


• [9] B. Sroysang, More on some Hardy type integral inequalities, J. Math. Inequal., 8 (2014), 497–501.
  • View Article
  • MathSciNet
  • Google Scholar