This note concerns explicitly quasiconvex set-valued maps, defined on a nonempty convex subset of a real linear space with values in a real linear space, partially ordered by a solid vectorially closed convex cone. It is shown that these generalized convex set-valued maps can be characterized in terms of classical explicit quasiconvexity of certain scalar functions.
A note on scalar characterization of explicitly quasiconvex set-valued maps / D. La Torre, N. Popovici, M. Rocca. - In: JOURNAL OF NONLINEAR AND CONVEX ANALYSIS. - ISSN 1345-4773. - 12:1(2011), pp. 113-118.
A note on scalar characterization of explicitly quasiconvex set-valued maps
D. La TorrePrimo
;
2011
Abstract
This note concerns explicitly quasiconvex set-valued maps, defined on a nonempty convex subset of a real linear space with values in a real linear space, partially ordered by a solid vectorially closed convex cone. It is shown that these generalized convex set-valued maps can be characterized in terms of classical explicit quasiconvexity of certain scalar functions.
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