Inequalities for discrete higher order convex functions

نویسنده

  • ANDRÁS PRÉKOPA
چکیده

[1] E. BOROS AND A. PRÉKOPA, Closed Form Two-Sided Bounds for Probabilities That Exactly r and at Least r out of n Events Occur, Mathematics of Operations Research, 14 (1989), 317–342. [2] D. DAWSON AND A. SANKOFF, An Inequality for Probabilities, Proceedings of the American Mathematical Society, 18 (1967), 504–507. [3] H.P. EDMUNDSON, Bounds on the Expectation of a Convex Function of a Random Variable, The RAND Corporation, P–982, April 9, 1957. [4] M. FRÉCHET, Les Probabilités Associées à un Système d’Événement Compatibles et Dépendants, Actualités Scientifiques Industrielles, Nos. 859, 942, Paris, 1940, 1943. [5] A. GILÁNYI AND ZS. PÁLES, On Convex Functions of Higher Order, Math. Inequalities and Appl., 11 (2008), 271–282. [6] A. GOBERNA AND M.A. LOPEZ, Linear Semi-Infinite Optimization, Wiley, New York, 1998. [7] J.L. JENSEN, Sur les fonctions convexes et les inégalités entre les valeurs moyennes, Acta Math., 30 (1906), 175–193. [8] C. JORDAN, Calculus of Finite Differences, Chelsea Publishing Company, New York, 1947. [9] S. KARLIN AND W.J. STUDDEN, Tchebycheff Systems: With Applications in Analysis and Statistics, Interscience, New York, 1966. [10] J.H.B. KEMPERMAN, The General Moment Problem, a Geometric Approach, Ann. Math. Statist., 39 (1968), 93–122. [11] S.M. KWEREL, Most Stringent Bounds on Aggregated Probabilities of Partially Specified Dependent Probability Systems, Journal of the American Statistical Association, 70 (1975), 472–479. [12] C.E. LEMKE, The Dual Method for Solving the Linear Programming Problem, Naval Research Logistic Quarterly, 1 (1954), 36–47. [13] A. MADANSKY, Bounds on the Expectation of a Convex Function of a Multivariate Random Variable, Annals of Math. Stat., 30, 743–746. [14] P.J. OLVER, On Multivariate Interpolation, School of Math., Univ. of Minnesota, MN, 2005. [15] J. PEČARIĆ AND V. ČULJAK, Interpolation Polynomials and Convex Functions of Higher Order, Math. Inequalities and Appl., 5 (2002), 369–386. [16] T. POPOVICIU,Sur quelques propriétés des fonctions d’une ou de deux variables réelles, Mathematica (Cluj), 8 (1934), 1–85. [17] T. POPOVICIU,Les Fonctions Convexes. Actualités Scientifiques et Industrielles 992, Hermann, Paris, France, 1944. [18] A. PRÉKOPA, Boole–Bonferroni Inequalities and Linear Programming, Oper. Res., 36 (1988), 145– 162. [19] A. PRÉKOPA, The Discrete Moment Problem and Linear Programming, Discrete Applied Mathematics, 27 (1990), 235–254.

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تاریخ انتشار 2009