Some new refined Hardy type integral inequalities (original) (raw)

2015, arXiv: Classical Analysis and ODEs

Abstract

In this paper, by using Jensen's inequality and Chebyshev integral inequality, some generalizations and new refined Hardy type integral inequalities are obtained. In addition, the corresponding reverse relation are also proved.

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References (6)

  1. G. H. Hardy, Notes on a theorem of Hilbert, Math. Z., 6 (1920), 314317.
  2. N. Levinson, Generalizations of inequalities of Hardy and Littlewood, Duke Math. J., 31 (1964), 389394.
  3. W. T. Sulaiman, Some Hardy type integral inequalities, Appl. Math. Lett., 25 (2012), 520525.
  4. J. L. W. V. Jensen, Sur les fonctions convexes et les ingalits entre les valeurs moyennes, Acta Math. 30 (1906), 175193.
  5. D.S. Mitrinović, Analytic Inequalities, Springer-Verlag, Berlin, 1970.
  6. B. Sroysang, More on Some Hardy type integral inequalities, J. Math. Ineq. V.8, Num. 3 (2014), 497-501. Khaled Mehrez Departement of Mathematics, University of Kairaouan, ISSAT. Kasserine 1200, Tunisia. Email: k.mehrez@yahoo.fr Khaled Mehrez. Département de Mathématiques ISSATK, Kairouan 3000, Tunisia. E-mail address: k.mehrez@yahoo.fr