Naslov
On some inequalities of Jensen-Mc Shane's type on rectangle and applications

Autori
Čuljak, Vera ; Ivanković, Božidar ; Pečarić, Josip

Izvornik
Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti (0351-8639) 503 (2009); 87-106

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Jensen's inequality ; isotonic functional ; convex function ; Diaz-Metcalf inequality ; Fejer inequality ; Lupas inequality

Sažetak
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 \cite{; ; ; ; csimori}; ; ; ; , Feyer's and Lupa% \c{; ; ; ; s}; ; ; ; type inequality for a function of two variables, and Petrovi\'{; ; ; ; c}; ; ; ; 's type inequality for two nonnegative real n-tuples in \cite{; ; ; ; prvi}; ; ; ; . \bibitem{; ; ; ; prvi}; ; ; ; B. Ivankovi\'{; ; ; ; c}; ; ; ; , S. Izumino, J. Pe\v{; ; ; ; c}; ; ; ; ari\'{; ; ; ; c}; ; ; ; , and M. Tominaga, On an inequality of V. Csisz\'{; ; ; ; a}; ; ; ; r and \bibitem{; ; ; ; csimori}; ; ; ; V. Csisz\'{; ; ; ; a}; ; ; ; r and T. F. M\'{; ; ; ; o}; ; ; ; ri, The convexity method of proving moment type inequalities, \emph{; ; ; ; \ Stat.. Probab. Lett.}; ; ; ; \textbf{; ; ; ; 66}; ; ; ; (2004), no. 3, 303-313. T.F. M\'{; ; ; ; o}; ; ; ; ri for convex functions of two variables, \emph{; ; ; ; JIPAM}; ; ; ; . J. Inequal. Pure Appl. Math., \textbf{; ; ; ; 8}; ; ; ; (2007), no. 3, article 88. (electronic).

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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