Abstract

It is known that convex functions with values in an ordered Banach space Y, whose positive cone Y+Y_+ is normal, have the same continuity properties as real-valued convex functions. We show that normality of Y+Y_+ is not only sufficient, but also necessary for this.

Author information

Contact details are reproduced from the original publication and may be historical.

Libor Veselý

Dip. di Matematica, Università degli Studi, Via C. Saldini 50, 20133 Milano, Italy

libor.vesely@unimi.it

Keywords

  • Convex operator
  • vector-valued convex function
  • ordered normal linear space
  • normal cone

Mathematics Subject Classification

47H99; 46B40

References

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  4. W. Rudin: Functional Analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, New York (1974).Google Scholar

Suggested citation

A. Carioli, L. Veselý. “Normal Cones and Continuity of Vector-Valued Convex Functions.” Journal of Convex Analysis 20 (2013), No. 2, 495–500. https://doi.org/10.68381/jca20030

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Published by Heldermann Verlag, 2013. Rights now held by Banach Press.