# IJPAM: Volume 14, No. 2 (2004)

ON A WEIGHTED HARDY-HILBERT'S
TYPE INEQUALITY

Jia Weijian, Gao Mingzhe, Gao Xuemei
Department of Mathematics and Computer Science
Normal College
Jishou University
Jishou Hunan 416000, P.R. CHINA
e-mail: jwj1959@163.com
e-mail: mingzhegao1940@yahoo.com.cn
e-mail: xuemeigao1971@163.com

Abstract.In this paper, it is shown that Generalized Hardy-Hilbert's double series inequality with weights can be established by introducing a parameter ( and two positive and differentiable functions and in interval (0, +  . In particular, for case , the various new extensions of the classical Hilbert's inequality for double series are obtained. As applications, some important inequalities are built, when and are power function, logarithm function, inverse trigonometric function and exponent function.

Received: April 28, 2004

AMS Subject Classification: 26D15, 33B15

Key Words and Phrases: generalized Hardy-Hilbert's inequality, Hilbert's inequality, double series, weight function, beta function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 14
Issue: 2