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Journal of Convex Analysis 20 (2013), No. 2, 495--500
Copyright Heldermann Verlag 2013

Normal Cones and Continuity of Vector-Valued Convex Functions

Andrea Carioli
Via L. da Vinci 31/A, 20030 Senago (MI), Italy

Libor Vesely
Dip. di Matematica, Universit degli Studi, Via C. Saldini 50, 20133 Milano, Italy

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.

Keywords: Convex operator, vector-valued convex function, ordered normal linear space, normal cone.

MSC: 47H99; 46B40

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