Inequalities of Gruss 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 Gruss Type involving the p-HH-Norms in the Cartesian Product Space. Journal of Mathematical Inequalities, 3 (4). pp. 543-557. ISSN 1846-579X
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 |
| URI | https://vuir.vu.edu.au/id/eprint/4385 |
| Official URL | http://files.ele-math.com/articles/jmi-03-53.pdf |
| Subjects | Historical > Faculty/School/Research Centre/Department > School of Engineering and Science Historical > FOR Classification > 0101 Pure Mathematics Historical > SEO Classification > 970101 Expanding Knowledge in the Mathematical Sciences |
| Keywords | ResPubID17564, Gr¨uss inequality, ˇ Cebyˇsev functional, Cartesian product, semi-inner product |
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