Inequalities of Grüuss type involving the p-HH-norms in the Cartesian product space

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.