• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.563-572
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• 2009

In this paper, by introducing some parameters and using the way of weight function, a new integral inequality with a best constant factor is given, which is a relation between Hilbert's integral inequality and a Hilbert-type inequality. As applications, the equivalent form, the reverse forms and some particular inequalities are considered.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.425-431
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• 2006

In this paper, by introducing three parameters A, B and ${\lambda}$, and estimating the weight coefficient, we give a new extension of Hardy-Hilbert's inequality with a best constant factor, involving the Beta function. As applications, we consider its equivalent inequality.

• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.291-298
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• 2012

In this paper, by estimating the weight function, we give a new Hilbert-type inequality with the integral in whole plane. As its applications, we consider the equivalent and a particular result.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.307-314
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• 2010

By introducing a homogeneous kernel of 0-degree with an independent parameter and estimating the weight coefficient, a bilateral form of the Hilbert-type series inequality with a best constant factor is established.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.411-423
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• 2007

This paper deals with a reverse Hardy-Hilbert's inequality with a best constant factor by introducing two parameters ${\lambda}$ and ${\alpha}$. We also consider the equivalent form and the analogue integral inequalities. Some particular results are given.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.393-401
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• 2009

By introducing a parameter and estimating the weight coefficient, we obtain a new Hilbert-type integral inequality with a composite kernel and a best constant factor. As applications, we also consider its equivalent forms and reverse forms.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.281-288
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• 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.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.93-100
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• 2008

In this paper, by introducing some parameters and estimating the weight function, we give a new Hilbert-type integral inequality with a best constant factor. The equivalent inequality and the reverse forms are considered.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.131-152
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• 2010

In this paper, by introducing some parameters we establish an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series. As an application, the reverses, some particular results and their equivalent forms are considered.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.19-29
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• 2006

In this paper, we obtain some inequalities similar to Hilbert type. Some new inequalities are also given.