On some inequalities of Jensen-McShanes type on rectangle and applicationsReport as inadecuate

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Proceeding of the Croatian Academy of Sciences and Arts. Mathematical Sciences, No.503=16 July 2009. -

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.

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

Author: Vera Čuljak - orcid.org-0000-0002-6691-2112 ; Department of Mathematics, Faculty of Civil Engineering, University of Zagreb, Kac

Source: http://hrcak.srce.hr/


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