# IJPAM: Volume 57, No. 4 (2009)

ON HILBERT TYPE INTEGRAL INEQUALITY
AND APPLICATIONS

Yu Zhou, Mingzhe Gao
Department of Mathematics and Computer Science
Normal College
Jishou University
Jishou, Hunan, 416000, P.R. CHINA
e-mail: yuzhou863@126.com
e-mail: mingzhegao@163.com

Abstract.In this paper it is shown that a new Hilbert type integral inequality can be established by introducing an integral kernel function of the form , where . And the constant factor expressed by the Euler number and  is proved to be the best possible. As applications, some equivalent forms are given.