Geodesic
Generalized Convexity and Separation Theorems
Journal of convex analysis, Tome 14 (2007) no. 2, pp. 239-247 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 
@article{JCA_2007_14_2_JCA_2007_14_2_a1,
     author = {K. Nikodem and Z. P\'ales},
     title = {Generalized {Convexity} and {Separation} {Theorems}},
     journal = {Journal of convex analysis},
     pages = {239--247},
     year = {2007},
     volume = {14},
     number = {2},
     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/