Abstract

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

Author information

Contact details are reproduced from the original publication and may be historical.

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.

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Suggested citation

P. Fischer, Z. Slodkowski. “Monotonicity of the Integral Mean and Convex Functions.” Journal of Convex Analysis 8 (2001), No. 2, 489–509. https://doi.org/10.68381/jca08026

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Published by Heldermann Verlag, 2001. Rights now held by Banach Press LLC.