Talk:Gâteaux derivative

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[edit] 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)

[edit] 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)