
Journal of Convex Analysis 08 (2001), No. 2, 489510 Copyright Heldermann Verlag 2001 Monotonicity of the Integral Mean and Convex Functions P. Fischer Dept. of Mathematics and Statistics, University of Guelph, Guelph, Ont. N1G 2W1, Canada Z. Slodkowski Dept. of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, IL 606077045, U.S.A. A set A will be said convexly majorized by a set B if the integral mean of any convex function over A is not exceeding its mean over B. Sufficient conditions and necessary conditions are presented about this relation. Methods will be introduced which generate such sets A and B. [ Fulltextpdf (526 KB)] 