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On Certain Extension of Hilbert’s Integral Inequality with Best Constants

Yongjin Li|Bing He|Yu Lin
경북대학교 자연과학대학 수학과|2008.09|Kyungpook Mathematical Journal|제48권 제3호|pp. 457-463

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참고문헌

키워드

Hilbert’s integral inequalityWeight function.
주제분류수학

초록

In this paper, by introducing a new function with two parameters, we give another generalizations of the Hilbert’s integral inequality with a mixed kernel k(x, y) = 1/A(x+y)+B|x−y| and a best constant factors. As applications, some particular results with the best constant factors are considered.

Abstract

In this paper, by introducing a new function with two parameters, we give another generalizations of the Hilbert’s integral inequality with a mixed kernel k(x, y) = 1/A(x+y)+B|x−y| and a best constant factors. As applications, some particular results with the best constant factors are considered.

참고문헌 (12)

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  2. M. GAO, "On Hilbert’s inequality and its applications", J. Math. Anal. Appl, 212, pp.316~323 (1997)
  3. G. H. HARDY, "Note on a theorem of Hilbert", Math. Z, 6, pp.314~317 (1920)
  4. G. H. HARDY, "Inequalities" (1934), Cambridge University Press
  5. J. KUANG, "Applied inequalities(Chinese)" (1993), Hunan Education Press, Changsha
  6. J. KUANG, "On new extensions of Hilbert’s integral inequality", Math. Anal. Appl, 235, pp.608~614 (1999)
  7. Y. LI, "A new Hilbert-type integral inequality and the equivalent form" (2006), Int. J. Math. Math. Sci
  8. D. S. MITRINOVIC, "Inequalities involving functions and their integrals and derivatives" (1991), Kluwer Academic, Boston
  9. B. G. PACHPATTE, "Inequalities similar to the integral analogue of Hilbert’s inequality", Tamkang J. Math, 30, pp.139~146 (1999)
  10. W. T. SULAIMAN, "Four inequalities similar to Hardy-Hilbert’s integral inequality", JIPAM. J. Inequal. Pure Appl. Math, 7(2), pp.8~ (2006)
  11. B. YANG, "An extension of Hardy-Hilbert’s inequality(Chinese)", Chinese Ann. Math. Ser, 23, pp.247~254 (2002)
  12. B. YANG, "On the norm of an integral operator and applications", J. Math. Anal. Appl, 321, pp.182~192 (2006)

관련 논문AI추천

On a New Hilbert-type Integral InequalityDongmei Xin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제2호On a Relation to Hilbert’s Integral Inequality and a Hilbert- Type InequalityBicheng Yang경북대학교 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 Hilbert-type Integral Inequalities with the Homogenous Kernel of -4- degreeBing He, Qiliang Huang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제3호Hilbert-Type Integral Inequalities in the Whole Plane with the Non-homogeneous KernelDongmei Xin경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2014 · 제54권 제1호On a Reverse Hardy-Hilbert's InequalityBicheng Yang경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2007 · 제47권 제3호

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