IJPAM: Volume 57, No. 4 (2009)
A NEW HILBERT TYPE INEQUALITY FOR DOUBLE SERIES
Xiaozhou Shang
, Mingzhe Gao
Department of Mathematics and Computer Science
Normal College
Jishou University
Jishou, Hunan, 416000, P.R. CHINA
e-mail: jdsysxz003@163.com
e-mail: mingzhegao@163.com



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


Abstract.A new Hilbert type inequality for
double series can be established by introducing a proper logarithm
function. The weight function is estimated by means of the
Euler-Maclaurin summation formula. And the constant factor
is proved to be the best possible, where
£¬and
are the Euler numbers, viz.
, etc. As applications, some equivalent inequalities are
considered.
Received: November 8, 2009
AMS Subject Classification: 26D15
Key Words and Phrases: Hilbert-type inequality, double series, monotonous, sequence, Euler-Maclaurin
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 4