• Title, Summary, Keyword: Gr$\ddot{u}$ss Inequality

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A GRÜSS TYPE INTEGRAL INEQUALITY ASSOCIATED WITH GAUSS HYPERGEOMETRIC FUNCTION FRACTIONAL INTEGRAL OPERATOR

  • Choi, Junesang;Purohit, Sunil Dutt
    • Communications of the Korean Mathematical Society
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    • v.30 no.2
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    • pp.81-92
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    • 2015
  • In this paper, we aim at establishing a generalized fractional integral version of Gr$\ddot{u}$ss type integral inequality by making use of the Gauss hypergeometric function fractional integral operator. Our main result, being of a very general character, is illustrated to specialize to yield numerous interesting fractional integral inequalities including some known 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.

AN APPROXIMATION OF THE FOURIER SINE TRANSFORM VIA GRÜSS TYPE INEQUALITIES AND APPLICATIONS FOR ELECTRICAL CIRCUITS

  • DRAGOMIR, S.S.;KALAM, A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.6 no.1
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    • pp.33-45
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    • 2002
  • An approximation of the Fourier Sine Transform via Gr$\ddot{u}$ss, Chebychev and Lupaş integral inequalities and application for an electrical curcuit containing an inductance L, a condenser of capacity C and a source of electromotive force $E_0P$(t), where P (t) is an $L_2$-integrable function, are given.

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