• Title, Summary, Keyword: Hilbert-type integral inequality

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On a Relation to Hilbert's Integral Inequality and a Hilbert-Type Inequality

  • Yang, Bicheng
    • 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.

On a Hilbert-Type Integral Inequality with a Combination Kernel and Applications

  • Yang, Bicheng
    • 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.

The Hilbert-Type Integral Inequality with the System Kernel of-λ Degree Homogeneous Form

  • Xie, Zitian;Zeng, Zheng
    • 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.

A REFINEMENT OF GRÜSS TYPE INEQUALITY FOR THE BOCHNER INTEGRAL OF VECTOR-VALUED FUNCTIONS IN HILBERT SPACES AND APPLICATIONS

  • Buse Constantin;Cerone Pietro;Dragomir Sever Silvestru;Roumeliotis John
    • Journal of the Korean Mathematical Society
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    • v.43 no.5
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    • pp.911-929
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    • 2006
  • A refinement of $Gr\ddot{u}ss$ type inequality for the Bochner integral of vector-valued functions in real or complex Hilbert spaces is given. Related results are obtained. Application for finite Fourier transforms of vector-valued functions and some particular inequalities are provided.

DISCRETE MULTIPLE HILBERT TYPE INEQUALITY WITH NON-HOMOGENEOUS KERNEL

  • Ban, Biserka Drascic;Pecaric, Josip;Peric, Ivan;Pogany, Tibor
    • Journal of the Korean Mathematical Society
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    • v.47 no.3
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    • pp.537-546
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    • 2010
  • Multiple discrete Hilbert type inequalities are established in the case of non-homogeneous kernel function by means of Laplace integral representation of associated Dirichlet series. Using newly derived integral expressions for the Mordell-Tornheim Zeta function a set of subsequent special cases, interesting by themselves, are obtained as corollaries of the main inequality.