On generalized means and generalized convex functions. (English) Zbl 0325.26007


26A51 Convexity of real functions in one variable, generalizations
62C05 General considerations in statistical decision theory
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[1] Hardy, G. H., Littlewood, J. E., andPolya, G.,Inequalities, Cambridge University Press, Cambridge, England, 1934. · Zbl 0010.10703
[2] Avriel, M.,R-Convex Functions, Mathematical Programming, Vol. 2, pp. 309-323, 1972. · Zbl 0249.90063
[3] Martos, B.,Nem-Linéaris Programmozási Módzerek Hátoköre, MTA Közgazdasávtudományi Intézeténk Közlemenyei (in Hungarian), Budapest, Hungary, No. 20, 1966.
[4] Avriel, M., andZang, I.,Generalized Convex Functions with Applications in Nonlinear Programming, Mathematical Programs for Activity Analysis, Edited by P. Van Moeseke, Leuven University Press, Leuven, Belgium, 1974.
[5] Zang, I.,Generalized Convex Programming, Technion, Israel Institute of Technology, Haifa, Israel, Department of Chemical Engineering, Doctoral Thesis, 1974.
[6] Avriel, M.,Solution of Certain Nonlinear Programs Involving r-Convex Functions, Journal of Optimization Theory and Applications, Vol. 11, pp. 159-174, 1973. · Zbl 0247.90053
[7] Aczel, J.,Lectures on Functional Equations and Their Applications, Academic Press, New York, New York, 1966.
[8] Beckenbach, E. F., andBelman, R.,Inequalities (2nd Edition), Springer-Verlag, New York, New York, 1965.
[9] Ferguson, T. S.,Mathematical Statistics, A Decision Theoretic Approach, Academic Press, New York, New York, 1967. · Zbl 0153.47602
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