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Continuous selections and reflexive Banach spaces


Authors: Valentin Gutev and Stoyan Nedev
Journal: Proc. Amer. Math. Soc. 129 (2001), 1853-1860
MSC (2000): Primary 54C65, 54C60, 46A25; Secondary 54B20, 46B10, 26B25
DOI: https://doi.org/10.1090/S0002-9939-00-05740-3
Published electronically: November 3, 2000
MathSciNet review: 1814119
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Abstract:

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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Additional Information

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: https://doi.org/10.1090/S0002-9939-00-05740-3
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
Published electronically: November 3, 2000
Communicated by: James E. West
Article copyright: © Copyright 2000 American Mathematical Society

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