Question

Suppose $S^m$ is a contraction on a complete metric space $(X,d)$. I want to show that this implies $S$ has a unique fix-point.

score 97 · Answer 1 · 2015-02-13 10:14:54

97

Views

Suppose $S^m$ is a contraction on a complete metric space $(X,d)$. I want to show that this implies $S$ has a unique fix-point.

Published on 13 Feb 2015 - 10:14

score 423 · Answer 2 · 2015-02-14 07:28:40

423

Views

Find the fixed point of $\cos(x)$ (equivalently of $\cos(\cos(x))$) restricted to $[0,\frac \pi 2]$.

Published on 14 Feb 2015 - 7:28

score 479 · Answer 3 · 2015-02-17 19:19:12

479

Views

Proof of a fixed point theorem on the disk

Published on 17 Feb 2015 - 19:19

score 1.8k · Answer 4 · 2015-02-18 22:50:44

1.8k

Views

If $f$ is a homeomorphism then any periodic point have period less or equal 2

Published on 18 Feb 2015 - 22:50

score 3.6k · Answer 5 · 2015-02-20 08:00:27

3.6k

Views

Example of contraction mapping

Published on 20 Feb 2015 - 8:00

score 56 · Answer 6 · 2026-03-28 15:11:27

56

Views

How do I show that infinite application of this function gives a constant?

Published on 28 Mar 2026 - 15:11

score 22 · Answer 7 · 2015-02-25 15:07:10

22

Views

Verify (without Banach Contraction Priciple), that the function g(x) = 1 + x - (1/8)x^3 has a unique fixed point

Published on 25 Feb 2015 - 15:07

score 46 · Answer 8 · 2015-02-25 17:20:32

46

Views

$f (x)=\exp(x/2)−25x^2$. Show that f on $ (4\log(20), \infty)$ has exactly one root.

Published on 25 Feb 2015 - 17:20

score 103 · Answer 9 · 2015-02-26 20:50:17

103

Views

Noisy contraction mapping

Published on 26 Feb 2015 - 20:50

score 104 · Answer 10 · 2015-02-26 23:10:48

104

Views

Atiyah-Bott fixed point formula; signs

Published on 26 Feb 2015 - 23:10

score 151 · Answer 11 · 2015-02-27 19:23:37

151

Views

Which of the followings have a fixed point?

Published on 27 Feb 2015 - 19:23

score 125 · Answer 12 · 2026-03-28 20:11:37

125

Views

Unclear passage of a theorem concerning compact operators (Schauder fixed point theorem)

Published on 28 Mar 2026 - 20:11

score 139 · Answer 13 · 2015-03-01 01:00:30

139

Views

Example of a function, so that $g(x)\neq x$

Published on 01 Mar 2015 - 1:00

score 120 · Answer 14 · 2026-03-27 16:26:54

120

Views

Deriving the fixed point for $\omega$ (i.e. $\lambda x.xx$) and proving it to be so

Published on 27 Mar 2026 - 16:26

score 2.4k · Answer 15 · 2015-03-07 06:02:21

2.4k

Views

Can't there be more than one fixed points in a contraction? or none?

Published on 07 Mar 2015 - 6:02

List Question

Suppose $S^m$ is a contraction on a complete metric space $(X,d)$. I want to show that this implies $S$ has a unique fix-point.

Find the fixed point of $\cos(x)$ (equivalently of $\cos(\cos(x))$) restricted to $[0,\frac \pi 2]$.

Proof of a fixed point theorem on the disk

If $f$ is a homeomorphism then any periodic point have period less or equal 2

Example of contraction mapping

How do I show that infinite application of this function gives a constant?

Verify (without Banach Contraction Priciple), that the function g(x) = 1 + x - (1/8)x^3 has a unique fixed point

$f (x)=\exp(x/2)−25x^2$. Show that f on $ (4\log(20), \infty)$ has exactly one root.

Noisy contraction mapping

Atiyah-Bott fixed point formula; signs

Which of the followings have a fixed point?

Unclear passage of a theorem concerning compact operators (Schauder fixed point theorem)

Example of a function, so that $g(x)\neq x$

Deriving the fixed point for $\omega$ (i.e. $\lambda x.xx$) and proving it to be so

Can't there be more than one fixed points in a contraction? or none?

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