Question

Find a condition for being the $f$ Gateaux differentiable at $0$, and that, consequently,the derivative of Gateaux is not necesarily linear map

score 59 · Answer 1 · 2026-04-15 13:24:56

Find a condition for being the $f$ Gateaux differentiable at $0$, and that, consequently,the derivative of Gateaux is not necesarily linear map

score 379 · Answer 2 · 2026-04-13 01:30:09

379

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Riesz isomorphism and Gateaux derivatives

Published on 13 Apr 2026 - 1:30

score 199 · Answer 3 · 2026-04-20 12:24:07

199

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Show that a function is nowhere Gateaux differentiable.

Published on 20 Apr 2026 - 12:24

score 96 · Answer 4 · 2026-04-13 04:51:05

96

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show that $(y^* \circ F) * \gamma(x) = \int_X {y^* \circ F(x+t)}d\gamma(t)$ is Gateaux differentiable everywhere

Published on 13 Apr 2026 - 4:51

score 66 · Answer 5 · 2026-04-06 06:17:19

66

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Definition of $\nabla f(ux_n - S(t))$ on a Banach space

Published on 06 Apr 2026 - 6:17

score 77 · Answer 6 · 2015-11-09 00:53:35

77

Views

Show that $f=1/2 ||T(x)||^2$ is Gateaux differentiable everywhere.

Published on 09 Nov 2015 - 0:53

score 303 · Answer 7 · 2026-05-05 03:02:51

303

Views

Is $ \left| \lim_{t \rightarrow 0}{\frac{f(x+ty) - f(x)}{t}} \right| \leq \lim_{t \rightarrow 0}{ \frac{|f(x+ty) - f(x)|}{|t|}}$

Published on 05 May 2026 - 3:02

score 36 · Answer 8 · 2026-04-10 06:35:30

36

Views

existence directional derivatives

Published on 10 Apr 2026 - 6:35

score 1.8k · Answer 9 · 2026-05-11 00:46:32

1.8k

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Show that $G(y^)(h) = \int \limits _X {y^ \circ F(t) \Bbb d \nu _h (t)}$ for some measure $\nu$ on $X$

Published on 11 May 2026 - 0:46

score 45 · Answer 10 · 2026-04-02 21:26:33

45

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well defined $F(u)=\int_I \psi udx$ and it's Gateaux derivative is $DF(u)=\psi(u)$

Published on 02 Apr 2026 - 21:26

score 54 · Answer 11 · 2026-04-19 14:54:58

54

Views

$F$ with Gateaux-derivative $A$, then $pF(u)=A(u)(u)$

Published on 19 Apr 2026 - 14:54

score 344 · Answer 12 · 2026-03-25 21:29:59

344

Views

Is this function Gateaux differentiable?

Published on 25 Mar 2026 - 21:29

score 195 · Answer 13 · 2026-04-30 14:32:13

195

Views

Show the mapping is $C^1$

Published on 30 Apr 2026 - 14:32

score 263 · Answer 14 · 2026-04-10 04:26:09

263

Views

Understanding the right assumption about Gateaux derivative in Banach spaces

Published on 10 Apr 2026 - 4:26

score 1.1k · Answer 15 · 2026-04-10 19:42:18

1.1k

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Counterexample for the Chain rule for the Gateaux-derivative

Published on 10 Apr 2026 - 19:42

List Question

Find a condition for being the $f$ Gateaux differentiable at $0$, and that, consequently,the derivative of Gateaux is not necesarily linear map

Riesz isomorphism and Gateaux derivatives

Show that a function is nowhere Gateaux differentiable.

show that $(y^* \circ F) * \gamma(x) = \int_X {y^* \circ F(x+t)}d\gamma(t)$ is Gateaux differentiable everywhere

Definition of $\nabla f(ux_n - S(t))$ on a Banach space

Show that $f=1/2 ||T(x)||^2$ is Gateaux differentiable everywhere.

Is $ \left| \lim_{t \rightarrow 0}{\frac{f(x+ty) - f(x)}{t}} \right| \leq \lim_{t \rightarrow 0}{ \frac{|f(x+ty) - f(x)|}{|t|}}$

existence directional derivatives

Show that $G(y^)(h) = \int \limits _X {y^ \circ F(t) \Bbb d \nu _h (t)}$ for some measure $\nu$ on $X$

well defined $F(u)=\int_I \psi udx$ and it's Gateaux derivative is $DF(u)=\psi(u)$

$F$ with Gateaux-derivative $A$, then $pF(u)=A(u)(u)$

Is this function Gateaux differentiable?

Show the mapping is $C^1$

Understanding the right assumption about Gateaux derivative in Banach spaces

Counterexample for the Chain rule for the Gateaux-derivative

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