Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On a Hilbert-Type Integral Inequality with a Combination Kernel and Applications

  • Yang, Bicheng (Department of Mathematics, Guangdong Education Institute)
  • Received : 2009.07.07
  • Accepted : 2009.08.21
  • Published : 2010.06.30
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Abstract

By introducing some parameters and using the way of weight function and the technic of real analysis and complex analysis, a new Hilbert-type integral inequality with a best constant factor and a combination kernel involving two mean values is given, which is an extension of Hilbert's integral inequality. As applications, the equivalent form and the reverse forms are considered.

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References

  1. G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge Univ. Press, Cambridge, 1952.
  2. D. S. Mintrinovic, J. E. Pecaric and A. M. Kink, Inequalities involving functions and their integrals and derivertives, Kluwer Academic Publishers, Boston, 1991.
  3. Bicheng Yang, On a generalization of the Hilbert's type inequality and its applications, Chinese Journal of Engineering Mathematics, 21, 5(2004), 821-824.
  4. Bicheng Yang, Ilko Brnetic, Mario Krnic and Josip Pecaric, Generalization of Hilbert and Hardy-Hilbert integral inequalities, Mathematical Inequalities and Applications, 8, 2(2005), 259-272.
  5. Yongjin Li and Bing He, A new Hilbert-type integral inequality and the equivalent form, Internat. J. Math. & Math. Soc., Vol.2006, Arc. ID 457378:1-6.
  6. Chune Xie, Best generalization of a new Hilbert-type inequality, Journal of Jinan University (Natural Science), 28, 1(2007), 24-27.
  7. Xiaokui Ge, New extension of a Hilbert-type integral inequality, Journal of Jinan University (Natural Science), 28, 5(2007), 447-450.
  8. Yongjin Li and Bing He, On inequalities of Hilbert's type, Bulletin of the Australian Mathematical Society, 76(2007), 1-13. https://doi.org/10.1017/S0004972700039423
  9. Yuquang Zhong, Complex analysis, Higher Education Press, Beijin, 2003.
  10. Jichang Kuang, Applied Inequalities, Shangdong Science Press, Jinan, 2004.
  11. Jichang Kuang, Introduction to real analysis, Hunan Education Press, Changsha, 1996