JournalszaaVol. 15, No. 4pp. 999–1013

ϵk0\epsilon k^0-Subdifferentia1s of Convex Functions

  • E.-Ch. Henkel

    Universität Halle-Wittenberg, Germany
$\epsilon k^0$-Subdifferentia1s of Convex Functions cover
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Abstract

The paper as a contribution to convex analysis in ordered linear topological spaces. For any convex function ff from a Banach space XX into a partially ordered one YY endowed with a convex cone KK some properties of the ϵk0\epsilon k^0-subdifferential ϵk0f(x)\partial ^≥_{\epsilon k^0}f(x) of ff are examined. The non-emptyness of ϵk0f(x)\partial ^≥_{\epsilon k^0}f(x) is proved, whenever YY is a normal order complete vector lattice and ff belongs to the class of functions which are continuous and convex with respect to the cone KK. For the real-valued case Bronsted and Rockafellar have proved that the set of subgradients of a lower semicontinuous function f on a Banach space XX is dense in the set of ϵ\epsilon-subgradients [21]. We deduce a similar result for a class of ϵk0\epsilon k^0-subdifferentials of functions which takes values in an ordered linear topological space YY.

Cite this article

E.-Ch. Henkel, ϵk0\epsilon k^0-Subdifferentia1s of Convex Functions. Z. Anal. Anwend. 15 (1996), no. 4, pp. 999–1013

DOI 10.4171/ZAA/742