List questions from contraction-operator

Published on 06 Jun 2020 - 21:13

78

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For a contraction mapping $T$ with a fixed point $x$, prove $\lvert T^{n}x_{0} -x \rvert \leq \lvert T^{n}x_{0} - T^{m}x_{0} \rvert $ where $0<m<n$

Published on 24 Jun 2020 - 7:08

57

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Criterion for a contractive mapping to map its domain into itself

Published on 24 Jun 2020 - 21:27

42

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Show that $T : C([-1,1],\mathbb{R}) \to C([-1,1],\mathbb{R})$ is a contraction

Published on 03 Jul 2020 - 3:01

146

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Questions about contraction

Published on 06 Jul 2020 - 2:39

93

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Contraction Mapping maps boundary on boundary?

Published on 17 Jul 2016 - 2:16

219

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Contractions mappings bijective maps boundarys on boundarys?

Published on 17 Jul 2016 - 18:48

97

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$T$ be a contraction on an infinite complete metric space , then is there a non singleton compact subset of $X$ which is invariant under $T$?

Published on 05 Aug 2016 - 16:19

207

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Non-linear contraction mapping

Published on 25 Mar 2026 - 6:51

61

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Justify for a simple $l_\infty$ contraction, $-(f_i(x)-f_i(x_o)) \leq \min\limits_ik |x_i-{x_o}_i|$

Published on 22 Oct 2016 - 3:51

407

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Multivariate Newton's method - how to apply the chain rule to $g(x)=x-(D_xf)^{-1}f(x)$

Published on 21 Mar 2026 - 22:55

744

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Proof that Bellman Optimality Operator converges

Published on 07 Nov 2016 - 17:42

79

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Isn't $[1,\infty)$ complete?

Published on 10 Nov 2016 - 18:32

180

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Given contraction in $\|\cdot \|_2$ norm, what is the contraction in $\|\cdot\|_\infty$ norm?

Published on 16 Nov 2016 - 6:41

1.6k

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Under what condition is a linear mapping contractive in the sup-norm?

Published on 27 Nov 2016 - 4:43

List Question

Conditions for a minimization mapping to be a contraction

For a contraction mapping $T$ with a fixed point $x$, prove $\lvert T^{n}x_{0} -x \rvert \leq \lvert T^{n}x_{0} - T^{m}x_{0} \rvert $ where $0<m<n$

Criterion for a contractive mapping to map its domain into itself

Show that $T : C([-1,1],\mathbb{R}) \to C([-1,1],\mathbb{R})$ is a contraction

Questions about contraction

Contraction Mapping maps boundary on boundary?

Contractions mappings bijective maps boundarys on boundarys?

$T$ be a contraction on an infinite complete metric space , then is there a non singleton compact subset of $X$ which is invariant under $T$?

Non-linear contraction mapping

Justify for a simple $l_\infty$ contraction, $-(f_i(x)-f_i(x_o)) \leq \min\limits_ik |x_i-{x_o}_i|$

Multivariate Newton's method - how to apply the chain rule to $g(x)=x-(D_xf)^{-1}f(x)$

Proof that Bellman Optimality Operator converges

Isn't $[1,\infty)$ complete?

Given contraction in $\|\cdot \|_2$ norm, what is the contraction in $\|\cdot\|_\infty$ norm?

Under what condition is a linear mapping contractive in the sup-norm?

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