Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On a Reverse of the Slightly Sharper Hilbert-type Inequality

  • Zhong, Jianhua (Department of Mathematics, Guangdong Institute of Education)
  • Received : 2008.11.12
  • Accepted : 2009.03.10
  • Published : 2009.12.31
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Abstract

In this paper, by introducing parameters ${\lambda}$, ${\alpha}$and two pairs of conjugate exponents (p, q), (r, s) and applying the improved Euler-Maclaurin's summation formula, we establish a reverse of the slightly sharper Hilbert-type inequality. As applications, the strengthened version and the equivalent form are given.

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References

  1. G. H. Hardy, J. E. Litterwood and G. Polya, Inequalities, Cambridge Univ Press Cambridge, 1952.
  2. D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Inequalities involving functions and their integrals and derivatives, Mathematics and its Applications, 53. Kluwer Academic Publishers Group, Dordrecht, 1991.
  3. J. Kuang, On new extensions of Hilbert's integral inequality, J. Math. Anal. Appl., 235(1999), 608-614. https://doi.org/10.1006/jmaa.1999.6373
  4. B. Yang, On an extension of Hardy-Hilbert's inequality, Chinese Annals of Math., 23A(2)(2002), 247-254 (in Chinese).
  5. B. Yang, On generalizations of Hardy-Hilbert's inequality and their equivalent forms, J. Math., 24(1)(2004), 24-30 (in Chinese).
  6. B. Yang, On a new extension of Hilbert's inequality with some parameters, Acta MathHungar., 108(4)(2005), 337-350.
  7. B. Yang, A more accurate hardy-hilbert's type inequality, Journal of Xnyang Nrmal Uiversity(Natural science edition), 18(2)(2005), 140-142.
  8. B. Yang, On a reverse of the Hardy-Hilbert's type inequality[J]., Inequalities Theory and Applications, 4(2004).
  9. B. Yang, A Reverse of the Hardy-Hilbert's Type Inequality, Mathematics in practice and theory., 36(11)(2006), 207-212.
  10. B. Yang and G. Wang, Some inequalities on harmonic series, J. Math. Study, 29(3)(1996), 90-97, (Chinese).
  11. B. Yang, Inequalities on the Hurwitz Zeta-Function Restricted to the Axis of Positive Reals, 36(1997), no. 36, 30-35.
  12. J. Kuang, Applied Inequalities, 3rd edition, Shandong Science and Technology Press, Jinan City, China, 2004.