##  [Fréchet Differentiability](/frechet-differentiability) 

  ##  [Fréchet Differentiability](https://puremath.quantumdictionary.io/frechet-differentiability-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A strong notion of differentiability for functions between normed vector spaces: at a point x the function f admits a bounded linear operator L (the Fréchet derivative) such that f(x+h)-f(x)-L(h)=o(‖h‖) as h→0, i.e. L uniformly approximates the first-order increment of f.