# A New Hilbert-type Integral Inequality with Some Parameters and Its Reverse

• Xie, Zitian ;
• Yang, Bicheng
• Published : 2008.03.31
• 27 2

#### Abstract

In this paper, by introducing some parameters and estimating the weight function, we give a new Hilbert-type integral inequality with a best constant factor. The equivalent inequality and the reverse forms are considered.

#### Keywords

Hilbert-type integral inequality;weight function;H$\"{o}$lder's inequality;equivalent inequality;reverse form

#### References

1. G. H. Hardy, J. E.Littlewood and G. P´olya, Inequalities, Cambridge University Press, Cambridge, 1952.
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3. D. S. Mintrinovic, J. E. Pecaric and A. M. Fink, Inequalities involving functions and their integrals and Derivertives, Kluwer Academic Publishers, Boston, 1991.
4. Bicheng Yang, On Hardy-Hilbert's integral inequality, J. Math. Anal. Appl., 261(2001), 295-306. https://doi.org/10.1006/jmaa.2001.7525
5. Bicheng Yang, On the extended Hilbert's integral inequality, Journal of Inequalities in Pure and Applied Mathmatics, 5(4)(2004), Article 96.
6. Bicheng Yang, Ilko Bnaetic, Mario Krnic and Josip Pecaric, Generalization of Hilbert and Hardy-Hilbert integral inequalities, Mathematical Inequalities and Applications, Mathematical Inequalities and Applications, 8(2)(2005), 259-272.
7. Jichang Kang, 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
2. On the Hilbert Type Integral Inequalities with Some Parameters and Its Reverse vol.49, pp.4, 2009, https://doi.org/10.5666/KMJ.2009.49.4.623