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30 June 2005 On the range of the derivative of a smooth mapping between Banach spaces
Robert Deville
Abstr. Appl. Anal. 2005(5): 499-507 (30 June 2005). DOI: 10.1155/AAA.2005.499

Abstract

We survey recent results on the structure of the range of the derivative of a smooth mapping f between two Banach spaces X and Y. We recall some necessary conditions and some sufficient conditions on a subset A of (X,Y) for the existence of a Fréchet differentiable mapping f from X into Y so that f(X)=A. Whenever f is only assumed Gâteaux differentiable, new phenomena appear: for instance, there exists a mapping f from 1() into 2, which is bounded, Lipschitz-continuous, and so that for all x,y1(), if xy, then f(x)f(y)>1.

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Robert Deville. "On the range of the derivative of a smooth mapping between Banach spaces." Abstr. Appl. Anal. 2005 (5) 499 - 507, 30 June 2005. https://doi.org/10.1155/AAA.2005.499

Information

Published: 30 June 2005
First available in Project Euclid: 25 July 2005

zbMATH: 1106.46023
MathSciNet: MR2201040
Digital Object Identifier: 10.1155/AAA.2005.499

Rights: Copyright © 2005 Hindawi

Vol.2005 • No. 5 • 30 June 2005
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