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On some inequalities of Jensen-Mc Shane's type on rectangle and applications (CROSBI ID 141552)

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Čuljak, Vera ; Ivanković, Božidar ; Pečarić, Josip On some inequalities of Jensen-Mc Shane's type on rectangle and applications // Rad Jugoslavenske akademije znanosti i umjetnosti. Razred za matematičke, fizičke i tehničke znanosti. Matematičke znanosti, 503 (2009), 87-106

Podaci o odgovornosti

Čuljak, Vera ; Ivanković, Božidar ; Pečarić, Josip

engleski

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

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).

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

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Podaci o izdanju

503

2009.

87-106

objavljeno

0351-8639

Povezanost rada

Matematika

Poveznice