List questions from frechet-derivative

Published on 09 Nov 2021 - 23:28

124

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What is the Fréchet derivative of a matrix eigenvalue?

Published on 11 Nov 2021 - 3:32

194

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Prove that $L(f)(x)$ is Fréchet differentiable.

Published on 18 Nov 2021 - 2:45

262

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Fréchet Derivative of a functional in $L^2$

Published on 20 Nov 2021 - 14:44

148

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Where is the $\Vert \cdot \Vert_{\infty}$ norm Fréchet differentiable on $c_0$?

Published on 27 Mar 2026 - 13:27

76

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Is this Fréchet derivative really a bounded functional?

Published on 26 Nov 2021 - 12:21

65

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Converse to Taylor's theorem in Banach spaces

Published on 11 Dec 2021 - 1:47

62

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Apply the mean value theorem to find $x_0$ with $\varphi(g(b))-\varphi(g(a))=\varphi'(g(x_0))(g(b)-g(a))$

Published on 28 Dec 2021 - 19:43

258

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When an ordinary partial derivative is a Frechet derivative on a Banach space?

Published on 06 Jan 2022 - 12:14

83

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Help proving that the derivative $Df(x)$ is continuous

Published on 27 Mar 2026 - 13:19

344

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How to express the Frechet derivative in terms of a gradient vector.

Published on 16 Jan 2022 - 1:43

26

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Symmetry of second derivatives: Can we conclude $({\rm D}_2({\rm D}_1f)(x)h_2)h_1'=({\rm D}_1({\rm D}_2f)(x)h_1)h_2'$?

Published on 21 Jan 2022 - 20:44

25

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For which class $H$ of functions is $H\ni x\mapsto\int_0^Tf(t,x(t))\:{\rm d}t$ differentiable?

Published on 26 Jan 2022 - 7:13

52

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How can we show that $x(t)-y(t)=\int_{s-ε}^tf(x(r),a)-f(y(r),a(r))\:{\rm d}r$ implies $x(s)-y(s)=(f(x(s),a)-f(x(s),\alpha(s)))\varepsilon+o(ε)$?

Published on 29 Jan 2022 - 20:37

190

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Chain rule for differentiation yields conflicting dimensions

Published on 07 Feb 2022 - 20:11

List Question

Prove that $DL(x)=L(x)$.

What is the Fréchet derivative of a matrix eigenvalue?

Prove that $L(f)(x)$ is Fréchet differentiable.

Fréchet Derivative of a functional in $L^2$

Where is the $\Vert \cdot \Vert_{\infty}$ norm Fréchet differentiable on $c_0$?

Is this Fréchet derivative really a bounded functional?

Converse to Taylor's theorem in Banach spaces

Apply the mean value theorem to find $x_0$ with $\varphi(g(b))-\varphi(g(a))=\varphi'(g(x_0))(g(b)-g(a))$

When an ordinary partial derivative is a Frechet derivative on a Banach space?

Help proving that the derivative $Df(x)$ is continuous

How to express the Frechet derivative in terms of a gradient vector.

Symmetry of second derivatives: Can we conclude $({\rm D}_2({\rm D}_1f)(x)h_2)h_1'=({\rm D}_1({\rm D}_2f)(x)h_1)h_2'$?

For which class $H$ of functions is $H\ni x\mapsto\int_0^Tf(t,x(t))\:{\rm d}t$ differentiable?

How can we show that $x(t)-y(t)=\int_{s-ε}^tf(x(r),a)-f(y(r),a(r))\:{\rm d}r$ implies $x(s)-y(s)=(f(x(s),a)-f(x(s),\alpha(s)))\varepsilon+o(ε)$?

Chain rule for differentiation yields conflicting dimensions

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