Geodesic
Normal Cones and Continuity of Vector-Valued Convex Functions
Journal of convex analysis, Tome 20 (2013) no. 2, pp. 495-5 Cet article a éte moissonné depuis la source Heldermann Verlag

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It is known that convex functions with values in an ordered Banach space Y, whose positive cone Y+ is normal, have the same continuity properties as real-valued convex functions. We show that normality of Y+ is not only sufficient, but also necessary for this.
Classification : 47H99, 46B40
Mots-clés : Convex operator, vector-valued convex function, ordered normal linear space, normal cone 
@article{JCA_2013_20_2_JCA_2013_20_2_a10,
     author = {A. Carioli and L. Vesely},
     title = {Normal {Cones} and {Continuity} of {Vector-Valued} {Convex} {Functions}},
     journal = {Journal of convex analysis},
     pages = {495--5},
     year = {2013},
     volume = {20},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2013_20_2_JCA_2013_20_2_a10/}
}
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A. Carioli; L. Vesely. Normal Cones and Continuity of Vector-Valued Convex Functions. Journal of convex analysis, Tome 20 (2013) no. 2, pp. 495-5. http://geodesic.mathdoc.fr/item/JCA_2013_20_2_JCA_2013_20_2_a10/