Proceedings of the American Mathematical Society

Author(s): Valentin Gutev; Stoyan Nedev
Journal: Proc. Amer. Math. Soc. 129 (2001), 1853-1860.
MSC (2000): Primary 54C65, 54C60, 46A25; Secondary 54B20, 46B10, 26B25
Posted: November 3, 2000
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Every l.s.c. mapping $\Phi$ 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.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 54C65, 54C60, 46A25, 54B20, 46B10, 26B25

Valentin Gutev
Affiliation: School of Mathematical and Statistical Sciences, Faculty of Science, University of Natal, King George V Avenue, Durban 4041, South Africa
Email: gutev@scifs1.und.ac.za

Stoyan Nedev
Affiliation: Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bontchev Str., bl. 8, 1113 Sofia, Bulgaria
Email: nedev@math.bas.bg

DOI: 10.1090/S0002-9939-00-05740-3
PII: S 0002-9939(00)05740-3
Keywords: Set-valued mapping, selection, lower semi-continuous, weakly continuous, hyperspace topology, convex function
Received by editor(s): November 18, 1995
Received by editor(s) in revised form: September 27, 1999
Posted: November 3, 2000
Communicated by: James E. West
Copyright of article: Copyright 2000, American Mathematical Society

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