Linearization representation
Theorem
$X,Y$ … Banach spaces with topology
$f\in C(X,Y)$
postulate
$ f(x+y) = f(x) + \int_0^1\ Df(x+t\ y)\cdot y\ \mathrm d t $
Discussion
$ f(x) = f(0) + \int_0^1\ Df(t\ x)\cdot x\ \mathrm d t $
Reference
Parents
Context
Fréchet derivative
,
Function integral
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