Original Article
Kyungpook Mathematical Journal 2010; 50(2): 281-288
Published online June 23, 2010
Copyright © Kyungpook Mathematical Journal.
On a Hilbert-Type Integral Inequality with a Combination
Kernel and Applications
Bicheng Yang
Department of Mathematics, Guangdong Education Institute, Guangzhou, Guang- dong 510303, P. R. China
Received: June 23, 2010; Revised: June 23, 2010; Accepted: June 23, 2010
By introducing some parameters and using the way of weight function and
the technic of real analysis and complex analysis, a new Hilbert-type integral inequality
with a best constant factor and a combination kernel involving two mean values is given,
which is an extension of Hilbert's integral inequality. As applications, the equivalent form
and the reverse forms are considered.
Keywords: Hilbert-type integral inequality, weight function, parameter