List questions from contraction-operator

Published on 04 Jun 2017 - 21:41

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Does there exist $x$, $y \in \mathbb{N}$ such that $x^2 − y^2 = 19$

Published on 10 Jun 2017 - 13:55

229

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If $x,y$ are distinct real numbers

Published on 10 Jun 2017 - 22:55

769

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Derivative-based sufficient conditions for contraction mappings for multivariate continuous functions

Published on 12 Jun 2017 - 0:56

311

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Show that $Tx = y - \alpha f(x) x$ is a contraction

Published on 28 Jul 2017 - 5:49

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Fastest way showing the limit exists without finding the limit?

Published on 31 Aug 2017 - 16:54

111

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Basic notions on contraction mapping theorem

Published on 21 Sep 2017 - 13:02

158

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Contraction Mapping Theorem Existence

Published on 09 Oct 2017 - 18:25

1.2k

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Show integral operator is contraction mapping

Published on 24 Oct 2017 - 20:21

159

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An integral functional on $C[0,1]$ is contractive

Published on 06 Nov 2017 - 4:21

96

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Finding the adjoint of matrix of operators

Published on 13 Nov 2017 - 14:41

80

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smallest constant $c$ for which: $|x^k - y^k| < c \cdot |x - y|$, with $x,y < 1/2$

Published on 17 Dec 2017 - 13:47

624

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Show that the integral equation $x(t) $ has a unique solution in C[a,b] for sufficiently small $\lambda$.

Published on 24 Dec 2017 - 21:55

515

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Let $T:C[0,1] \to C[0,1]:Tx(t) = \int_0^t x(s)ds$. Is it a contraction? Is any power of T a contraction?

Published on 24 Dec 2017 - 22:37

560

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an example of a complete space $X$ and a such mapping $T$ without fixed points & Show that if $X$ is compact then such $T$ has a unique fixed point.

Published on 24 Dec 2017 - 23:21

List Question

Proof of Discrete Markus-Yamabe Conjecture for Triangular Systems

Does there exist $x$, $y \in \mathbb{N}$ such that $x^2 − y^2 = 19$

If $x,y$ are distinct real numbers

Derivative-based sufficient conditions for contraction mappings for multivariate continuous functions

Show that $Tx = y - \alpha f(x) x$ is a contraction

Fastest way showing the limit exists without finding the limit?

Basic notions on contraction mapping theorem

Contraction Mapping Theorem Existence

Show integral operator is contraction mapping

An integral functional on $C[0,1]$ is contractive

Finding the adjoint of matrix of operators

smallest constant $c$ for which: $|x^k - y^k| < c \cdot |x - y|$, with $x,y < 1/2$

Show that the integral equation $x(t) $ has a unique solution in C[a,b] for sufficiently small $\lambda$.

Let $T:C[0,1] \to C[0,1]:Tx(t) = \int_0^t x(s)ds$. Is it a contraction? Is any power of T a contraction?

an example of a complete space $X$ and a such mapping $T$ without fixed points & Show that if $X$ is compact then such $T$ has a unique fixed point.

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