Talk:Gateaux derivative

Michal-Bastiani differentiability

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)

Example not clear

The example of $x^{3}/(x^{2}+y^{2})$ because the derivation is not described. One might think $dF={\frac {\partial F}{\partial x}}dx+{\frac {\partial F}{\partial y}}dy$

Non-linearity

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)

I think I'm wrong to say that. At any case I'd clarify a bit the difference between the two. 18.83.1.20 18:32, 2 November 2007 (UTC)

Gâteaux derivative - Gâteaux differential and Gâteaux variation

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:

• Gâteaux variation: http://eom.springer.de/G/g043370.htm
• Gâteaux differential: http://eom.springer.de/G/g043370.htm
• Gâteaux derivative: http://eom.springer.de/G/g043360.htm

Thanks Amelio Vázquez (talk) 20:58, 10 January 2008 (UTC)

This issues seems to have been cleared up in the edits of User:Garygateaux around 2009. Brent Perreault (talk) 21:02, 20 December 2012 (UTC)

Proposing merger with "Differentiation in Frechet spaces"

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

The result is Do not merge

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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 discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Requested move 1 February 2019

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this section.

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)

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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)

• Support. I added (translated) content to René Gateaux from the French article so it now likewise has a note about the confusion. 94.21.204.175 (talk) 11:36, 1 February 2019 (UTC)
• Support. French language Wikipedia discusses the spelling issue, and the primary sources used on this page show the name without the circumflex. tamasys (talk) 03:24, 5 February 2019 (UTC)

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The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Definition

The limit should be taken from above. Otherwise it would be needless to look at two opposite directions. You can read it here: Gateaux Differentiability Revisited | Applied Mathematics & Optimization (springer.com) 141.23.199.23 (talk) 10:37, 8 October 2024 (UTC)