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Inequalities of Gruss Type involving the p-HH-Norms in the Cartesian Product Space

Kikianty, Eder and Dragomir, Sever S and Cerone, Pietro (2009) Inequalities of Gruss Type involving the p-HH-Norms in the Cartesian Product Space. Journal of Mathematical Inequalities, 3 (4). pp. 543-557. ISSN 1846-579X

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Abstract

Inequalities in estimating a type of ˇ Cebyˇsev functional involving the p-HH-norms are obtained by applying the known results by Gr¨uss, Ostrowski, ˇ Cebyˇsev, and Lupas¸. Some of these inequalities are proven to be sharp. In 1998, Dragomir and Fedotov considered a generalised ˇ Cebyˇsev functional, in order to approximate the Riemann-Stieltjes integral. In this paper, some sharp bounds for the generalised ˇ Cebyˇsev functional with convex integrand and monotonically increasing integrator are established as well. An application for the ˇ Cebyˇsev functional involving the p-HH-norms is also considered; and the bounds are proven to be sharp.

Item Type: Article
Uncontrolled Keywords: ResPubID17564, Gr¨uss inequality, ˇ Cebyˇsev functional, Cartesian product, semi-inner product
Subjects: Faculty/School/Research Centre/Department > School of Engineering and Science
FOR Classification > 0101 Pure Mathematics
SEO Classification > 970101 Expanding Knowledge in the Mathematical Sciences
Depositing User: VUIR
Date Deposited: 03 May 2012 06:07
Last Modified: 03 May 2012 06:07
URI: http://vuir.vu.edu.au/id/eprint/4385
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