Inequalities of Grüss Type Involving the p-HH-Norms in the Cartesian Product Space

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Kikianty, Eder, Dragomir, Sever S and Cerone, Pietro (2009) Inequalities of Grüss Type Involving the p-HH-Norms in the Cartesian Product Space. Research report collection, 12 (1).

Abstract

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

Item type Article
URI https://vuir.vu.edu.au/id/eprint/17677
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords Grüss inequality, Čebyšev functional, Cartesian product, semi-inner product
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