The paper as a contribution to convex analysis in ordered linear topological spaces. For any convex function from a Banach space into a partially ordered one endowed with a convex cone some properties of the -subdifferential of are examined. The non-emptyness of is proved, whenever is a normal order complete vector lattice and belongs to the class of functions which are continuous and convex with respect to the cone . 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 is dense in the set of -subgradients . We deduce a similar result for a class of -subdifferentials of functions which takes values in an ordered linear topological space .
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E.-Ch. Henkel, -Subdifferentia1s of Convex Functions. Z. Anal. Anwend. 15 (1996), no. 4, pp. 999–1013DOI 10.4171/ZAA/742