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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Differentiation of real-valued functions and continuity of metric projections


Author: Simon Fitzpatrick
Journal: Proc. Amer. Math. Soc. 91 (1984), 544-548
MSC: Primary 46G05; Secondary 49A52, 58C20, 58C25
MathSciNet review: 746087
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Abstract: We characterize the Fréchet differentiability of real-valued functions on certain real Banach spaces in terms of a directional derivative being equal to a modified version of the local Lipschitz constant. This yields the continuity of metric projections onto closed sets whose distance functions have directional derivatives equal to 1, provided the Banach space and its dual have Fréchet differentiable norms.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0746087-9
PII: S 0002-9939(1984)0746087-9
Article copyright: © Copyright 1984 American Mathematical Society