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Fréchet derivative
Set
| $X,Y$ … Banach spaces with topology |
| $\mathcal O$ … open in $X$ |
| $D:\mathrm{Continuous}(\mathcal O,Y)\to \mathrm{Continuous}(\mathcal O,\mathrm{BoundedLinOp}(X,Y))$ |
| $Df:=x\mapsto J_x^f$ |
For $J_x f$, see Linear approximation.
Discussion
This definition does nothing more than emphasizing the functionality of $L_x^f$ in $f$.
Reference
Wikipedia: Derivative of a function, Fréchet derivative
Parents
Requirements
