title: Improvements of Jensen-Type Inequalities for Diamond-α Integrals.
abstract: We give further improvements of the Jensen inequality and its converse on time scales, allowing also negative weights. These results generalize the Jensen inequality and its converse for both discrete and continuous cases. Further, we investigate the exponential and logarithmic convexity of the differences between the left-hand side and the right-hand side of these inequalities and present several families of functions for which these results can be applied.
authors.affiliation: School of Natural Sciences, National University of Sciences and Technology, Islamabad 44000, Pakistan.
authors.forename: Rabia
authors.identifier: 0000-0002-3464-7115
authors.initials: R
authors.lastname: Bibi
authors.affiliation: Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb, Croatia.
authors.forename: Josip
authors.initials: J
authors.lastname: Pečarić
authors.affiliation: Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb, Croatia.
authors.forename: Mirna Rodić
authors.initials: MR
authors.lastname: Lipanović