On the K-continuity of K-hull midconvex set-valued functions
| Autor: | Antonella Fiacca, Susanna Vercillo |
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| Jazyk: | English<br />French<br />Italian |
| Rok vydání: | 1993 |
| Předmět: | |
| Zdroj: | Le Matematiche, Vol 48, Iss 2, Pp 263-271 (1993) |
| Druh dokumentu: | article |
| ISSN: | 0373-3505 2037-5298 |
| Popis: | In the present paper it is proved the K-continuity of a set-valued function which is K-hull midconvex, K-lower semicontinuous at a point and whose values are bounded K-midconvex sets; the concept of K-hull midconvexity is introduced here and it is weaker than the one of K-midconvexity. Then a generalization of the well known Theorem of Bernstein-Doech is obtained, which gives, in the particular case when the space is locally bounded, a characterization of the K-continuity of set-valued function. The theorems presented here improve some earlier results obtained by K. Nikodem (Zeszyty Nauk Politech. Lodz 559, Rospravy Mat. 114, 1989). |
| Databáze: | Directory of Open Access Journals |
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