Kyungpook Mathematical Journal

  • 제49권2호
  • /
  • Pages.393-401
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  • 2009
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On a New Hilbert-type Integral Inequality

  • Xin, Dongmei (Department of Mathematics, Guangdong Institute of Education)
  • 투고 : 2008.09.19
  • 심사 : 2009.01.09
  • 발행 : 2009.06.30
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초록

By introducing a parameter and estimating the weight coefficient, we obtain a new Hilbert-type integral inequality with a composite kernel and a best constant factor. As applications, we also consider its equivalent forms and reverse forms.

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참고문헌

  1. G. H. Hardy, J. E. Littlewood, G. Polya, Inequalities, Cambridge University Press, Cambridge, UK, 1952.
  2. Bicheng Yang, On a generalization of the Hilbert's type inequality and its applications, Chinese Journal of Engineering Mathematics, 21(4)(2004), 821-824.
  3. Bicheng Yang, Hongwei Liang, A new Hilbert-type inequality with a parameter, Journal of Henan University (Natural Science), 35(4)(2005), 4-8.
  4. Bicheng Yang, On the norm of an integral operator and applications, J. Math. Anal. Appl., 321(2006), 182-192. https://doi.org/10.1016/j.jmaa.2005.07.071
  5. ZhuxiWang, Dunrin Guo, An introduction to special functions, Science Press, Beijing, 1979.
  6. Jichang Kuang, Applied inequalities. Shangdong Science and Technology, Press, Jinan, 2004.

피인용 문헌

  1. A New Hilbert-type Inequality with the Integral in Whole Plane vol.52, pp.3, 2012, https://doi.org/10.5666/KMJ.2012.52.3.291