A reverse Hilbert-type inequality with a generalized homogeneous kernel

Main Article Content

Bing He

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.

Article Details

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
Section
Papers
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.