NDLI: Differentiation of Real-Valued Functions and Continuity of Metric Projections

Content Provider	Scilit
Author	Fitzpatrick, Simon
Copyright Year	1984
Description	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.
Related Links	http://www.ams.org/proc/1984-091-04/S0002-9939-1984-0746087-9/S0002-9939-1984-0746087-9.pdf
Ending Page	548
Page Count	5
Starting Page	544
ISSN	00029939
e-ISSN	10886826
DOI	10.2307/2044798
Journal	Proceedings of the American Mathematical Society
Issue Number	4
Volume Number	91
Language	English
Publisher	Duke University Press
Access Restriction	Open
Subject Keyword	Metric Projections Valued Functions Real Valued Continuity Differentiation of Real
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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Differentiation of Real-Valued Functions and Continuity of Metric Projections