Geodesic
Monotonicity of the Integral Mean and Convex Functions
Journal of convex analysis, Tome 8 (2001) no. 2, pp. 489-51 
P. Fischer; Z. Slodkowski. Monotonicity of the Integral Mean and Convex Functions. Journal of convex analysis, Tome 8 (2001) no. 2, pp. 489-51. http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a11/
@article{JCA_2001_8_2_JCA_2001_8_2_a11,
     author = {P. Fischer and Z. Slodkowski},
     title = {Monotonicity of the {Integral} {Mean} and {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {489--51},
     year = {2001},
     volume = {8},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2001_8_2_JCA_2001_8_2_a11/}
}
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Voir la notice de l'article provenant de la source Heldermann Verlag

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.