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JMB Journal of Microbiolog and Biotechnology

OPEN ACCESS eISSN 0454-8124
pISSN 1225-6951
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Original Article

Kyungpook Mathematical Journal 2009; 49(4): 731-742

Published online December 23, 2009

Copyright © Kyungpook Mathematical Journal.

On a Reverse of the Slightly Sharper Hilbert-type Inequality

Jianhua Zhong

Department of Mathematics, Guangdong Institute of Education, Guangzhou, 510303, P. R. China

Abstract

In this paper, by introducing parameters $lambda$, $alpha$ and two pairs of conjugate exponents $(p,q)$, $(r,s)$ and applying the improved Euler-Maclaurin's summation formula, we establish a reverse of the slightly sharper Hilbert-type inequality. As applications, the strengthened version and the equivalent form are given.

Keywords: ilbert-type inequality, weight coefficient, conjugate exponent, Euler-Maclaurin's summation formula, H"{o}lder's inequality