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ISSN 1088-6826(e) ISSN 0002-9939(p)

Porosity and differentiability in smooth Banach spaces

Author(s): Pando Gr. Georgiev
Journal: Proc. Amer. Math. Soc. 133 (2005), 1621-1628.
MSC (2000): Primary 49J53; Secondary 49J50
Posted: January 14, 2005
MathSciNet review: 2120263
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Abstract: We improve a result of Preiss, Phelps and Namioka, showing that every submonotone mapping in a Gateaux smooth Banach space is single-valued on the complement of a $\sigma$ -cone porous subset. If a Banach space has a uniformly $\beta$ -differentiable Lipschitz bump function (with respect to some bornology $\beta$ ), then we show with a much simpler argument (localization of $\delta$ -minimum of a perturbed function) that every continuous convex function on is $\beta$ -differentiable on the complement of a $\sigma$ -uniformly porous set.

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Additional Information:

Pando Gr. Georgiev
Affiliation: Department of Mathematics and Informatics, Sofia University ``St. Kl. Ohridski", 5 James Bourchier Boulevard, 1126 Sofia, Bulgaria
Address at time of publication: Electrical & Computer Engineering and Computer Science Department, University of Cincinnati, ML 0030, Cincinnati, Ohio 45220
Email: pgeorgie@ececs.uc.edu

DOI: 10.1090/S0002-9939-05-07736-1
PII: S 0002-9939(05)07736-1
Keywords: Porous set, submonotone mappings, differentiability
Received by editor(s): July 31, 2002
Posted: January 14, 2005
Dedicated: Dedicated to Professor Petar Kenderov on the occasion of his {60}th anniversary
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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