IJPAM: Volume 14, No. 2 (2004)
Department of Mathematics and Computer Science
Jishou Hunan 416000, P.R. CHINA
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