Continuous selections and reflexive Banach spaces

被引：6
|
作者：
Gutev, V
Nedev, S
机构：
[1] Univ Natal, Fac Sci, Sch Math & Stat Sci, ZA-4041 Durban, South Africa
[2] Bulgarian Acad Sci, Inst Math, BU-1113 Sofia, Bulgaria
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2001年 / 129卷 / 06期
关键词：
set-valued mapping; selection; lower semi-continuous; weakly continuous; hyperspace topology; convex function;
D O I：
10.1090/S0002-9939-00-05740-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Every l.s.c. mapping Phi from a space X into the non-empty closed convex subsets of a reflexive Banach space Y 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.
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页码：1853 / 1860
页数：8
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