Original scientific paper

On some inequalities of Jensen-McShane's type on rectangle and applications

Vera Čuljak orcid.org/0000-0002-6691-2112 ; Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Kaciceva 26, 10 000 Zagreb, Croatia
Božidar Ivanković ; Faculty of transport and traffic engineering, University of Zagreb, Vukeli´ceva 4, 10 000 Zagreb, Croatia
Josip Pečarić ; Faculty of Textile Technology, University of Zagreb, Pierottijeva 6, 10 000 Zagreb, Croatia

Abstract

In this paper we provide the sequence of inequalities which include McShane’s generalization of Jensen’s inequality for normalized isotonic positive linear functional and convex (concave) function defined on a rectangle. As applications, for different choice of functionals
F , we present the refinements of the recent results: Diaz-Metcalf’s type inequality for bounded random variables in [2], Feyer’s and Lupas type inequality for a function of two variables, and Petrovic’s type inequality for two nonnegative real n-tuples in [6].

Keywords

Jensen’s inequality; isotonic functional; convex function; Diaz-Metcalf inequality; Fejer inequality; Lupas inequality; Petrovic inequality

Hrčak ID:

110233

URI

https://hrcak.srce.hr/110233

Publication date:

1.7.2009.

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