A classical result by Crouzeix (1977) states that a real-valued function is convex if and only if any function obtained from it by adding a linear functional is quasiconvex. The principal aim of this paper is to present a similar characterization for certain cone-convex set-valued functions by means of cone-quasiconvex and affine set-valued functions.

A Characterization of Cone-Convexity for Set-Valued Functions by Cone-Quasiconvexity

ROCCA, MATTEO
2015-01-01

Abstract

A classical result by Crouzeix (1977) states that a real-valued function is convex if and only if any function obtained from it by adding a linear functional is quasiconvex. The principal aim of this paper is to present a similar characterization for certain cone-convex set-valued functions by means of cone-quasiconvex and affine set-valued functions.
http://www.springer.com/math/analysis/journal/11228
Cone-convexity; Cone-quasiconvexity; Rådström’s cancellation law; Set-valued affine function;
Kuroiwa, Daishi; Popovici, Nicolae; Rocca, Matteo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2023990
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