Geodesic
Generalized Convexity and Separation Theorems
Journal of convex analysis, Tome 14 (2007) no. 2, pp. 239-247.

Voir la notice de l'article provenant de la source Heldermann Verlag

Kakutani's classical theorem (stating that two disjoint convex sets can be separated by complementary convex sets) is extended to the setting when convexity is meant in the sense of Beckenbach. Then a characterization of pairs of functions that can be separated by a generalized convex function or by a function belonging to a two-parameter family (in the sense of Beckenbach) is presented. As consequences, stability results of the Hyers-Ulam-type are also obtained.
Classification : 26A51, 52A01, 39B62
Mots-clés : Generalized convex sets, generalized convex functions, separation theorems 
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     author = {K. Nikodem and Z. P\'ales},
     title = {Generalized {Convexity} and {Separation} {Theorems}},
     journal = {Journal of convex analysis},
     pages = {239--247},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_2_JCA_2007_14_2_a1/}
}
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K. Nikodem; Z. Páles. Generalized Convexity and Separation Theorems. Journal of convex analysis, Tome 14 (2007) no. 2, pp. 239-247. http://geodesic.mathdoc.fr/item/JCA_2007_14_2_JCA_2007_14_2_a1/