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Paper Title:
A New Hardy-Hilbert's Type Inequality for Double Series and its Applications
Author(s):
Mingzhe Gao
Department of Mathematics and Computer Science, Normal College Jishou University,
Jishou Hunan, 416000,
People's Republic of China
mingzhegao1940@yahoo.com.cn
Abstract:
In this paper, it is shown that a new Hardy-Hilbert’s type
inequality for double series can be established by introducing a parameter and the weight function of the form
where c is Euler
constant and
And
the coefficient is proved to be the
best possible. And as the mathematics aesthetics, several important constants
and
appear simultaneously in the coefficient and the weight
function when
In particular, for
case
some new Hilbert’s
type inequalities are obtained. As applications, some extensions of Hardy-Littlewood’s inequality are given.
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