Question

Gateaux but not Frechet differentiable functional

score 1.5k · Answer 1 · 2026-04-09 19:21:04

1.5k

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Gateaux but not Frechet differentiable functional

Published on 09 Apr 2026 - 19:21

score 550 · Answer 2 · 2026-04-12 14:57:22

550

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On the Definition of Gateaux Derivative

Published on 12 Apr 2026 - 14:57

score 301 · Answer 3 · 2026-04-11 03:17:22

301

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Gateaux and Frechet derivatives on $\mathbb{R}^2$.

Published on 11 Apr 2026 - 3:17

score 541 · Answer 4 · 2026-04-13 09:58:28

541

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Gateaux derivative vs Frechet derivative - what is the essential difference?

Published on 13 Apr 2026 - 9:58

score 117 · Answer 5 · 2026-04-14 15:37:15

117

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What is the derivative of the following functional?

Published on 14 Apr 2026 - 15:37

score 271 · Answer 6 · 2026-04-14 23:55:42

271

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How to prove $(\ell_1\ |.\|)$ is Gateaux differentiable at $x$ if and only if $x_i\not= 0$ for all $i\in\mathbf{N}$?

Published on 14 Apr 2026 - 23:55

score 109 · Answer 7 · 2026-04-17 07:28:14

109

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Let $f$ such that $\lim_{\varepsilon\rightarrow 0^+}\frac{f(x+\varepsilon y)-f(x)}{\varepsilon}=b+a\cdot y$ $\forall y$. Show that $b=0$.

Published on 17 Apr 2026 - 7:28

score 189 · Answer 8 · 2026-04-15 03:53:24

189

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I dont understand this statement: Prove that continuity in $x$ of the Gateaux derivative implies Frechet differentiability

Published on 15 Apr 2026 - 3:53

score 347 · Answer 9 · 2026-04-13 03:32:42

347

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Gateaux derivative of a functional $f:\mathbb{R}^2 \to \mathbb{R}$ and why the Frechet derivative of it does not exist

Published on 13 Apr 2026 - 3:32

score 1.1k · Answer 10 · 2026-04-14 08:19:52

1.1k

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Locally Lipschitz and Gâteaux Derivative if and only if Frechet Derivative

Published on 14 Apr 2026 - 8:19

score 3.2k · Answer 11 · 2026-04-09 20:34:44

3.2k

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What exactly is the difference between Gateaux derivative and directional derivative?

Published on 09 Apr 2026 - 20:34

score 5.7k · Answer 12 · 2026-04-17 02:41:52

5.7k

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Derivative of the matrix exponential with respect to its matrix argument

Published on 17 Apr 2026 - 2:41

score 1.8k · Answer 13 · 2026-04-14 05:38:40

1.8k

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Gateaux derivative of $L_p$ norm

Published on 14 Apr 2026 - 5:38

score 1.4k · Answer 14 · 2026-04-13 21:31:53

1.4k

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Prove that continuity in x of the Gateaux derivative, $f'(x;y)$, implies Frechet differentiability

Published on 13 Apr 2026 - 21:31

score 3.1k · Answer 15 · 2026-04-12 17:03:19

3.1k

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What is an example of Gâteaux differentiable but not Fréchet differentiable at a point in a finite-dimensional space?

Published on 12 Apr 2026 - 17:03

List Question

Gateaux but not Frechet differentiable functional

On the Definition of Gateaux Derivative

Gateaux and Frechet derivatives on $\mathbb{R}^2$.

Gateaux derivative vs Frechet derivative - what is the essential difference?

What is the derivative of the following functional?

How to prove $(\ell_1\ |.\|)$ is Gateaux differentiable at $x$ if and only if $x_i\not= 0$ for all $i\in\mathbf{N}$?

Let $f$ such that $\lim_{\varepsilon\rightarrow 0^+}\frac{f(x+\varepsilon y)-f(x)}{\varepsilon}=b+a\cdot y$ $\forall y$. Show that $b=0$.

I dont understand this statement: Prove that continuity in $x$ of the Gateaux derivative implies Frechet differentiability

Gateaux derivative of a functional $f:\mathbb{R}^2 \to \mathbb{R}$ and why the Frechet derivative of it does not exist

Locally Lipschitz and Gâteaux Derivative if and only if Frechet Derivative

What exactly is the difference between Gateaux derivative and directional derivative?

Derivative of the matrix exponential with respect to its matrix argument

Gateaux derivative of $L_p$ norm

Prove that continuity in x of the Gateaux derivative, $f'(x;y)$, implies Frechet differentiability

What is an example of Gâteaux differentiable but not Fréchet differentiable at a point in a finite-dimensional space?

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