Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On a New Hilbert-type Integral Inequality

  • Xin, Dongmei (Department of Mathematics, Guangdong Institute of Education)
  • Received : 2008.09.19
  • Accepted : 2009.01.09
  • Published : 2009.06.30
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Abstract

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.

Keywords

References

  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.

Cited by

  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