Some weighted Gruss-type inequalities with not necessarily positive weights on time scales

Abstract

The aim of this paper is to present weighted versions of some Gruss-type inequalities on time scales, using weights that are allowed to take some negative values, these are Hermite-Hadamard weights, the Steffensen-Popoviciu weights and the Gruss-Popoviciu weights. The notions of weighted integral mean, weighted variance and weighted covariance are expanded according to these weights. Some applications of these inequalities are presented.