• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.623-630
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• 2009

This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities with some parameters. We also consider the equivalent inequalities and the reverse forms.

• 대한수학회논문집
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• 제27권3호
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• pp.547-556
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• 2012

A new Hardy-Hilbert type integral inequality for double series with weights can be established by introducing a parameter ${\lambda}$ (with ${\lambda}>1-\frac{2}{pq}$) and a weight function of the form $x^{1-\frac{2}{r}}$ (with $r$ > 1). And the constant factors of new inequalities established are proved to be the best possible. In particular, for case $r$ = 2, a new Hilbert type inequality is obtained. As applications, an equivalent form is considered.