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Related to the discussion of linearity and continuity, it might be interesting to discuss the notion of "Michal-Bastiani differentiability" (see e.g. https://ncatlab.org/nlab/show/Michal-Bastiani%20smooth%20map). Nmdwolf ( talk) 14:34, 11 April 2022 (UTC)
The example of because the derivation is not described. One might think
I think it's a bit confusing to say Gateaux derivative isn't linear unlike Frechet derivative. Actually they both are linear as far as the function is concerned. Gateaux derivative isn't linear with respect to the "direction", the latter notion being meaningless for Frechet derivative. I don't think any statement in the article is false per se, just that the comparison is not very meaningful and misleading. 18.83.1.20 18:29, 2 November 2007 (UTC)
My understanding is that the definition is wrong and uncomplete. The article is in fact defining the Gâteaux differential, not the Gâteaux derivative. Both concepts are often confused in the literature. In addition, this article should distinguish between the following concepts:
Thanks Amelio Vázquez ( talk) 20:58, 10 January 2008 (UTC)
The two articles describe the same properties.
Since the technical term is Gateaux derivative, I propose keeping this the official title, while merging the rest of the information in, letting readers know that this is how one defines differentiation in Frechet spaces. — Preceding unsigned comment added by 128.120.104.8 ( talk) 20:02, 29 August 2014 (UTC)
oppose:See the subsection "Relation with the Fréchet derivative".-- 140.180.241.239 ( talk) 03:50, 19 November 2015 (UTC)
( non-admin closure)The result of the move request was: Page moved. ( closed by non-admin page mover) Warm Regards, ZI Jony (Talk) 18:19, 7 February 2019 (UTC)
The request to rename this article to Gateaux derivative has been carried out. |
Gâteaux derivative → Gateaux derivative – RG's name should be printed with no circumflex, as evidenced by the birth register of Vitry-le-François, see "Acte de naissance de René Eugène Gateaux, page 32/86 of year 1889, No. 61". archives.marne.fr. and the related French speaking Wikipédia articles. The (widely spread) misprint comes from a confusion with the common noun "gâteaux" (cakes). Glidepil ( talk) 09:13, 1 February 2019 (UTC)