IJPAM: Volume 53, No. 2 (2009)

A HILBERT-TYPE INEQUALITY WITH PARAMETER

Huang Zheng$^1$, Gao Mingzhe$^2$
$^{1,2}$Department of Mathematics and Computer Science
Normal College of Jishou University
Jishou University
Jishou Hunan, 416000, P.R. CHINA
$^{1}$e-mail: hnjdsyhz@126.com
$^{2}$e-mail: mingzhegao@163.com


Abstract.In this paper it is shown that a Hilbert-type inequality with parameter $ \lambda $ can be established by introducing a real functions $ u\left( x \right) $. In particular, two forms of the Hilbert-type inequality are combined into one similar form, when $ u(n) = n + {\lambda \over 2} \ne 0 $, where $ n \in N_0 $ and $ \lambda $ is an integer. As applications, some refinements on the Fejer-Riesz type inequality and the Hardy type inequality are given.

Received: April 25, 2009

AMS Subject Classification: 26D15

Key Words and Phrases: Hilbert-type inequality, double series, parameter, Blaschke Decomposition Theorem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 53
Issue: 2