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 56 · Answer 1 · 2015-09-23 10:28:38

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

score 376 · Answer 2 · 2015-10-09 19:19:01

376

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Riesz isomorphism and Gateaux derivatives

Published on 09 Oct 2015 - 19:19

score 197 · Answer 3 · 2015-11-04 11:50:00

197

Views

Show that a function is nowhere Gateaux differentiable.

Published on 04 Nov 2015 - 11:50

score 95 · Answer 4 · 2015-11-05 01:20:27

95

Views

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

Published on 05 Nov 2015 - 1:20

score 64 · Answer 5 · 2026-03-23 05:24:40

64

Views

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

Published on 23 Mar 2026 - 5:24

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 301 · Answer 7 · 2015-11-14 12:32:16

301

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 14 Nov 2015 - 12:32

score 32 · Answer 8 · 2026-03-25 17:06:39

32

Views

existence directional derivatives

Published on 25 Mar 2026 - 17:06

score 1.8k · Answer 9 · 2015-12-04 08:50:25

1.8k

Views

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 04 Dec 2015 - 8:50

score 44 · Answer 10 · 2015-12-15 20:49:27

44

Views

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

Published on 15 Dec 2015 - 20:49

score 52 · Answer 11 · 2026-03-13 16:17:40

52

Views

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

Published on 13 Mar 2026 - 16:17

score 343 · Answer 12 · 2016-01-09 08:42:48

343

Views

Is this function Gateaux differentiable?

Published on 09 Jan 2016 - 8:42

score 191 · Answer 13 · 2013-09-23 02:17:34

191

Views

Show the mapping is $C^1$

Published on 23 Sep 2013 - 2:17

score 260 · Answer 14 · 2014-03-09 11:02:31

260

Views

Understanding the right assumption about Gateaux derivative in Banach spaces

Published on 09 Mar 2014 - 11:02

score 1.1k · Answer 15 · 2014-03-09 21:25:05

1.1k

Views

Counterexample for the Chain rule for the Gateaux-derivative

Published on 09 Mar 2014 - 21:25

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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