|
|||||
|
|
Continuous selections and reflexive Banach spaces |
|
| Authors: | Valentin Gutev Stoyan Nedev |
| Institution: | School of Mathematical and Statistical Sciences, Faculty of Science, University of Natal, King George V Avenue, Durban 4041, South Africa ; Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bontchev Str., bl. 8, 1113 Sofia, Bulgaria |
| Abstract: | Every l.s.c. mapping |
| Keywords: | Set-valued mapping selection lower semi-continuous weakly continuous hyperspace topology convex function |
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文 | |
from a space 
into the non-empty closed convex subsets of a reflexive Banach space 
admits a continuous selection provided it satisfies a ``weak' u.s.c. condition. This result partially generalizes some known selection theorems. Also, it is successful in solving a problem concerning the set of proper lower semi-continuous convex functions on a reflexive Banach space.