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On a Reverse of the Slightly Sharper Hilbert-type Inequality

Jianhua Zhong
경북대학교 자연과학대학 수학과|2009.12|Kyungpook Mathematical Journal|제49권 제4호|pp. 731-742

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참고문헌

키워드

H¨older’s inequalityHilbert-type inequalityweight coefficientconjugate exponentEuler-Maclaurin’s summation formula
주제분류수학

초록

In this paper, by introducing parameters γ, α 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 givenper than inequality

Abstract

In this paper, by introducing parameters γ, α 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 givenper than inequality

참고문헌 (12)

  1. G. H. Hardy, "Inequalities" (1952), Cambridge Univ Press
  2. D. S. Mitrinovic, "Inequalities involving functions and their integrals and derivatives" (1991), Kluwer Academic Publishers Group
  3. J. Kuang, "On new extensions of Hilbert's integral inequality", J. Math. Anal. Appl, 235, pp.608~614 (1999)
  4. B. Yang, "On an extension of Hardy-Hilbert's inequality", Chinese Annals of Math, 23A(2), pp.247~254 (2002)
  5. B. Yang, "On generalizations of Hardy-Hilbert's inequality and their equivalent forms", J. Math, 24(1), pp.24~30 (2004)
  6. B. Yang, "On a new extension of Hilbert's inequality with some parameters", Acta MathHungar, 108(4), pp.337~350 (2005)
  7. B. Yang, "A more accurate hardy-hilbert's type inequality", Journal of Xnyang Nrmal Uiversity(Natural science edition), 18(2), pp.140~142 (2005)
  8. "Inequalities Theory and Applications", 2004, ~
  9. B. Yang, "A Reverse of the Hardy-Hilbert's Type Inequality", Mathematics in practice and theory, 36(11), pp.207~212 (2006)
  10. B. Yang, "Some inequalities on harmonic series", J. Math. Study, 29(3), pp.90~97 (1996)
  11. B. Yang, "Inequalities on the Hurwitz Zeta-Function", Restricted to the Axis of Positive Reals, 36, pp.30~35 (1997)
  12. J. Kuang, "Applied Inequalities" (2004), Shandong Science and Technology Press

관련 논문AI추천

A New Dual Hardy-Hilbert’s Inequality with some Parameters and its ReverseWuyi Zhong경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제3호A New Hilbert-type Integral Inequality with Some Parametersand Its ReverseBicheng Yang, Zitian Xie경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2008 · 제48권 제1호On a Relation to Hilbert’s Integral Inequality and a Hilbert- Type InequalityBicheng Yang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제3호On a Reverse Hardy-Hilbert's InequalityBicheng Yang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2007 · 제47권 제3호On a New Hilbert-type Integral InequalityDongmei Xin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제2호On the Hilbert Type Integral Inequalities with Some Param- eters and Its ReverseHuseyin Yildirim, Mehmet Zeki Sarikaya, Umut Mutlu Ozkan경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제4호

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