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