The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

A New Hardy-Hilbert's Type Inequality for Double Series and its Applications


Mingzhe Gao

Department of Mathematics and Computer Science, Normal College Jishou University,
Jishou Hunan, 416000,
People's Republic of China


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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