Reference Needed - Taylor's Theorem with Fréchet Derivatives

Question

According to Wikipedia, Taylor's Theorem holds for Fréchet derivatives, but no reference is given. I started looking in various books and they all mention that it is possible to write down a version of Taylor's theorems for Fréchet derivatives but no one seems to actually write it down.

Do you know of any precise reference?

See also Proving limit of f(x) - Tnf(x) (Taylor) is zero, in multivariable calculus. The proof follows easily with induction and the mean-value inequality. — peek-a-boo, Apr 11 '23 at 20:02

score 2 · Accepted Answer · answered Mar 28 '23 at 12:54

2

A classical reference is the book "Differential calculus" by Henri Cartan, around section 5.6.

answered Mar 28 '23 at 12:54

gerw

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Reference Needed - Taylor's Theorem with Fréchet Derivatives

1 Answers1