• 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.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.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.50 no.2
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• pp.297-306
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• 2010

In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree - $\lambda$ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.

• 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.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1261-1273
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• 2001

In this paper we prove a version of Gruss integral inequality for mappings with values in Hilbert spaces. Some applications for convex functions defined on Hibert space are also given.

• 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.48 no.3
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• pp.457-463
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• 2008

In this paper, by introducing a new function with two parameters, we give another generalizations of the Hilbert's integral inequality with a mixed kernel $k(x, y) = \frac {1}{A(x+y)+B{\mid}x-y{\mid}}$ and a best constant factors. As applications, some particular results with the best constant factors are considered.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.207-224
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• 2003

Some weighted Ostrowski type integral inequalities for vector-valued functions in Hilbert spaces are given. Applications for quadrature rules with values in Hilbert spaces are also pointed out.