On Semicontinuity of Convex-valued Multifunctions and Cesari’s Property (Q)
نویسنده
چکیده
We investigate two types of semicontinuity for set-valued maps, Painlevé–Kuratowski semicontinuity and Cesari’s property (Q). It is shown that, in the context of convexvalued maps, the concepts related to Cesari’s property (Q) have better properties than the concepts in the sense of Painlevé–Kuratowski. In particular, we give a characterization of Cesari’s property (Q) by means of upper semicontinuity of the scalarizations by the support function σf( · )(y∗) : X → R. We compare both types of semicontinuity and show their coincidence in special cases.
منابع مشابه
Semicontinuity of Convex-valued Multifunctions
We introduce semicontinuity concepts for functions f with values in the space C(Y ) of closed convex subsets of a finite dimensional normed vector space Y by appropriate notions of upper and lower limits. We characterize the upper semicontinuity of f : X → C(Y ) by the upper semicontinuity of the scalarizations σf( · )(y∗) : X → R by the support function. Furthermore, we compare our semicontinu...
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