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Journal of Convex Analysis 08 (2001), No. 2, 489--510
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 60607-7045, 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.

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