A reverse Hilbert-type inequality with a generalized homogeneous kernel

Authors

  • Bing He Independent Author

DOI:

https://doi.org/10.5556/j.tkjm.42.2011.484

Keywords:

Hilbert's integral inequality, Weight function, reverse Holder's inequality

Abstract

Inthispaper,by introducing a generalized homogeneous kernel and estimating the weight function,a new reverse Hilbert-type integral inequality with some parameters and a best constant factor is established.Furthermore, the corresponding equivalent form is considered.

Author Biography

Bing He, Independent Author

Department of Mathematics,

Guangdong Education College.

Lecturer

 

References

G. H. Hardy, J. E. Littlewood and G. Polya, Inequalities, Cambridge University Press, 1934.

D. S.Mitrinovic, J. E. Pecaric and A.M. Fink, Inequalities Involving Functions and Their Integrals andDerivatives, Kluwer Academic, Boston, 1991.

B. Yang, The Normof Operator and Hilbert-type Inequalities. Science Press, Beijing, 2009.

B. Yang, On a reverse Hardy-Hilbert’s inequality, KYUNGPOOK Math. J., 47(2007), 411–423.

Z. Xie and B. Yang, A new Hilbert-type integral inequality with some parameters and its reverse, Kyungpook Math. J., 48(2008), 93–100.

C. Zhao and L.Debnath,Some newinverse typeHilbert integral inequalities, Journal ofMathematical Analysis and Applications, 262(2001), 411–418.

J. Kuang, Applied Inequalities, Shangdong Science Press, Jinan, 2004.

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Published

2011-03-22

How to Cite

He, B. (2011). A reverse Hilbert-type inequality with a generalized homogeneous kernel. Tamkang Journal of Mathematics, 42(1), 1-7. https://doi.org/10.5556/j.tkjm.42.2011.484

Issue

Section

Papers