IJPAM: Volume 57, No. 4 (2009)
Department of Mathematics and Computer Science
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 úČand 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