1 jul. PDF | On Jul 1, , Rogério de Aguiar and others published Considerações sobre as derivadas de Gâteaux e Fréchet. In particular, then, Fréchet differentiability is stronger than differentiability in the Gâteaux sense, meaning that every function which is Fréchet differentiable is. 3, , no. 19, – A Note on the Derivation of Fréchet and Gâteaux. Oswaldo González-Gaxiola. 1. Departamento de Matemáticas Aplicadas y Sistemas. Author: Mezizuru Tegar Country: Greece Language: English (Spanish) Genre: Love Published (Last): 16 March 2017 Pages: 250 PDF File Size: 17.48 Mb ePub File Size: 19.95 Mb ISBN: 930-7-98618-447-1 Downloads: 41773 Price: Free* [*Free Regsitration Required] Uploader: Kihn Differentiation is a linear operation in the following sense: This is analogous to the result from basic complex analysis that a function is analytic if it is complex differentiable in an open set, and is a fundamental result in the study of infinite dimensional holomorphy.

## Gâteaux derivative

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### Gâteaux Derivative — from Wolfram MathWorld ### Gâteaux derivative – Wikipedia

And you have that. Riesz extension Riesz representation Open mapping Parseval’s identity Schauder fixed-point. We avoid adopting this convention here to allow examination of the widest possible class of pathologies. Suppose that F is C 1 in the sense that the mapping.

## Gâteaux Derivative

Linearity need not be assumed: Riesz extension Riesz representation Open mapping Parseval’s identity Schauder fixed-point. The limit appearing in 1 is taken relative to the topology of Y. frecbet The limit here is meant in the usual sense of a limit of a function defined on a metric space see Functions on metric spacesusing V and W as the two metric spaces, and the above frechef as the function of argument h in V. This definition is discussed in the finite-dimensional case in: Deriada, I just take it for example we’re learning multivariate calculus now, so I’m familiar with this definition.

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Many of the derivads familiar properties of the derivative follow from this, such as multilinearity and commutativity of the higher-order derivatives. Note that this is not the same as requiring that the map D f x: For instance, the following sufficient condition holds Hamilton Rather than a multilinear function, this is instead a homogeneous function of degree n in h.

So there are no fractions there. This page was last edited on 6 Octoberat The chain rule also holds as does the Leibniz rule whenever Y is an algebra and a TVS in which multiplication is continuous.