Open Access
2014 Reverses of the Jensen-Type Inequalities for Signed Measures
Rozarija Jakšić, Josip Pečarić, Mirna Rodić Lipanović
Abstr. Appl. Anal. 2014: 1-11 (2014). DOI: 10.1155/2014/626359


In this paper we derive refinements of the Jensen type inequalities in the case of real Stieltjes measure dλ, not necessarily positive, which are generalizations of Jensen's inequality and its reverses for positive measures. Furthermore, we investigate the exponential and logarithmic convexity of the difference between the left-hand and the right-hand side of these inequalities and give several examples of the families of functions for which the obtained results can be applied. The outcome is a new class of Cauchy-type means.


Download Citation

Rozarija Jakšić. Josip Pečarić. Mirna Rodić Lipanović. "Reverses of the Jensen-Type Inequalities for Signed Measures." Abstr. Appl. Anal. 2014 1 - 11, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022762
MathSciNet: MR3251532
Digital Object Identifier: 10.1155/2014/626359

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
Back to Top