title: Levinson's type generalization of the Jensen inequality and its converse for real Stieltjes measure.
abstract: We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi's inequality. The obtained results are then applied for establishing new mean-value theorems. The results from this paper represent a generalization of several recent results.
authors.affiliation: Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, Zagreb, 10000 Croatia.
authors.forename: Rozarija
authors.initials: R
authors.lastname: Mikić
authors.affiliation: Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, Zagreb, 10000 Croatia.
authors.forename: Josip
authors.initials: J
authors.lastname: Pečarić
authors.affiliation: Faculty of Textile Technology, University of Zagreb, Prilaz baruna Filipovića 28a, Zagreb, 10000 Croatia.
authors.forename: Mirna
authors.identifier: 0000-0001-7035-0186
authors.initials: M
authors.lastname: Rodić
keywords: Giaccardi’s inequality; Green function; Hermite-Hadamard’s inequality; Jensen’s inequality; Levinson’s inequality; converse Jensen’s inequality; mean-value theorems