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.
Normal cones and continuity of vector-valued convex functions / A. Carioli, L. Vesely. - In: JOURNAL OF CONVEX ANALYSIS. - ISSN 0944-6532. - 20:2(2013), pp. 495-500.
Normal cones and continuity of vector-valued convex functions
L. VeselyUltimo
2013
Abstract
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.
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