Question

Prove $\lim_{h \to 0^{+}}\frac{\lVert u +hv \rVert_{\infty} - \lVert u \rVert_{\infty}}{h}=\max_{x \in M}(v\cdot \operatorname{sign}(u))$

score 122 · Answer 1 · 2026-04-21 10:04:47

122

Views

Prove $\lim_{h \to 0^{+}}\frac{\lVert u +hv \rVert_{\infty} - \lVert u \rVert_{\infty}}{h}=\max_{x \in M}(v\cdot \operatorname{sign}(u))$

Published on 21 Apr 2026 - 10:04

score 895 · Answer 2 · 2026-05-06 12:29:00

895

Views

Lipschitz function which is Gâteaux-differentiable is Fréchet-differentiable

Published on 06 May 2026 - 12:29

score 135 · Answer 3 · 2026-05-05 15:22:57

135

Views

Differentiability of Norms of $l_{\infty}$

Published on 05 May 2026 - 15:22

score 59 · Answer 4 · 2026-05-05 14:09:59

59

Views

Find a counterexample that $f(x)$ is Gateaux differentiable and $\lambda(x)$ is not continous

Published on 05 May 2026 - 14:09

score 534 · Answer 5 · 2026-05-06 14:20:35

534

Views

Directional derivatives of matrix trace functionals

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score 50 · Answer 6 · 2026-05-06 05:43:39

50

Views

First Variation of CDF inside an Indicator Function

Published on 06 May 2026 - 5:43

score 170 · Answer 7 · 2026-04-23 11:02:15

170

Views

Derivative of a functional with respect to another functional

Published on 23 Apr 2026 - 11:02

score 54 · Answer 8 · 2026-05-05 14:25:36

54

Views

prove that the functional is $\alpha$-elliptic

Published on 05 May 2026 - 14:25

score 200 · Answer 9 · 2026-05-05 02:38:09

200

Views

Question regarding Gateaux differentiability

Published on 05 May 2026 - 2:38

score 886 · Answer 10 · 2026-05-05 12:48:56

886

Views

Taylor expansion for Gâteaux derivative

Published on 05 May 2026 - 12:48

score 668 · Answer 11 · 2026-05-05 13:04:23

668

Views

Necessity of the Hahn Banach Theorem for the Gateaux Mean Value Theorem

Published on 05 May 2026 - 13:04

score 512 · Answer 12 · 2026-05-10 13:50:11

512

Views

How to prove that Frechet derivative exists and coincides with the Gateau derivative?

Published on 10 May 2026 - 13:50

score 132 · Answer 13 · 2026-05-10 13:48:35

132

Views

Gateaux Derivative of Fourier Transform/Characteristic Function

Published on 10 May 2026 - 13:48

score 100 · Answer 14 · 2026-05-10 13:49:24

100

Views

Can a variational inequality (necessary condition for minima) be strict?

Published on 10 May 2026 - 13:49

score 593 · Answer 15 · 2026-05-10 14:55:51

593

Views

Frechet Derivative of a Function Containing an Integral Operator Applied to the Differentiated Term

Published on 10 May 2026 - 14:55

List Question

Prove $\lim_{h \to 0^{+}}\frac{\lVert u +hv \rVert_{\infty} - \lVert u \rVert_{\infty}}{h}=\max_{x \in M}(v\cdot \operatorname{sign}(u))$

Lipschitz function which is Gâteaux-differentiable is Fréchet-differentiable

Differentiability of Norms of $l_{\infty}$

Find a counterexample that $f(x)$ is Gateaux differentiable and $\lambda(x)$ is not continous

Directional derivatives of matrix trace functionals

First Variation of CDF inside an Indicator Function

Derivative of a functional with respect to another functional

prove that the functional is $\alpha$-elliptic

Question regarding Gateaux differentiability

Taylor expansion for Gâteaux derivative

Necessity of the Hahn Banach Theorem for the Gateaux Mean Value Theorem

How to prove that Frechet derivative exists and coincides with the Gateau derivative?

Gateaux Derivative of Fourier Transform/Characteristic Function

Can a variational inequality (necessary condition for minima) be strict?

Frechet Derivative of a Function Containing an Integral Operator Applied to the Differentiated Term

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