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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Fréchet vs. Gâteaux differentiability of Lipschitzian functions


Authors: Maria Gieraltowska-Kedzierska and F. S. Van Vleck
Journal: Proc. Amer. Math. Soc. 114 (1992), 905-907
MSC: Primary 26E15; Secondary 26A16, 46G05, 49J50
MathSciNet review: 1010805
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Abstract: Examples have been given of Lipschitzian functions that are Gâteaux-differentiable everywhere, but nowhere Fréchet-differentiable. One such example has been reported, mistakenly, in several papers as having domain in $ {L^2}([0,\pi ])$, when it should have been $ {L^1}([0,\pi ])$. We discuss this example.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1010805-X
Keywords: Fréchet differentiability, Gâteaux differentiability
Article copyright: © Copyright 1992 American Mathematical Society