IJPAM: Volume 57, No. 4 (2009)
ON HILBERT TYPE INTEGRAL INEQUALITY
AND APPLICATIONS
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



Normal College
Jishou University
Jishou, Hunan, 416000, P.R. CHINA


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.
Received: November 12, 2009
AMS Subject Classification: 26D15
Key Words and Phrases: Hilbert's integral inequality, integral kernel function, Euler number, weight function, the best constant
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 4