Generalized Convex Set-Valued Maps
نویسندگان
چکیده
The aim of this paper is to show that under a mild semicontinuity assumption (the so-called segmentary epi-closedness), the cone-convex (resp. cone-quasiconvex) set-valued maps can be characterized in terms of weak cone-convexity (resp. weak cone-quasiconvexity), i.e. the notions obtained by replacing in the classical definitions the conditions of type ”for all x, y in the domain and for all t in ]0, 1[ ...” by the corresponding conditions of type ”for all x, y in the domain there exists t in ]0, 1[ ...”.
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