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Generalized convex set-valued maps

✍ Scribed by Joël Benoist; Nicolae Popovici

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
164 KB
Volume
288
Category
Article
ISSN
0022-247X

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✦ Synopsis

The aim of this paper is to show that under a mild semicontinuity assumption (the so-called segmentary epi-closedness), the cone-convex (respectively, cone-quasiconvex) set-valued maps can be characterized in terms of weak cone-convexity (respectively, 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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