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Practice Problems for Revising Basic Results from Analysis

score 28 · Answer 1 · 2022-06-22 14:09:31

28

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Practice Problems for Revising Basic Results from Analysis

Published on 22 Jun 2022 - 14:09

score 160 · Answer 2 · 2026-03-30 12:22:36

160

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Convergence of Newton's method for Banach spaces

Published on 30 Mar 2026 - 12:22

score 177 · Answer 3 · 2022-07-03 21:11:03

177

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A proof of the sub-super solution method using Schauder's fixed point theorem

Published on 03 Jul 2022 - 21:11

score 87 · Answer 4 · 2022-07-08 00:19:06

87

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If $f\in \mathcal{C}(\mathbb{S}^n,\mathbb{S}^n)$ and $f$ is not surjective, then $f$ has a fixed point

Published on 08 Jul 2022 - 0:19

score 172 · Answer 5 · 2026-03-26 11:04:49

172

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Conditions for $I-x A$ to be a convergent matrix for some $x\in \mathbb{R}$

Published on 26 Mar 2026 - 11:04

score 91 · Answer 6 · 2022-07-10 05:48:52

91

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Cardinality of set $\{f\in C^1 (\mathbb R)\mid f(0)=0,f(2)=2, |f’(x)|\leq 3/2\}$

Published on 10 Jul 2022 - 5:48

score 122 · Answer 7 · 2026-03-25 20:09:42

122

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What are some examples of fixed point problems where transfinite constructions elucidated the problem?

Published on 25 Mar 2026 - 20:09

score 91 · Answer 8 · 2026-03-27 16:26:54

91

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Leray-Schauder Degree for Periodic Functions

Published on 27 Mar 2026 - 16:26

score 103 · Answer 9 · 2022-07-12 20:22:35

103

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If $f\in \mathcal{C}(\mathbb{S}^n,\mathbb{S}^n)$ and $\mathrm{deg}_2(f)=0$, then $f(x_0)=x_0$ and $f(y_0)=-y_0$ for some $x_0, y_0$.

Published on 12 Jul 2022 - 20:22

score 248 · Answer 10 · 2022-07-16 23:13:09

248

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Existence of a fixed point to a vector-valued mapping

Published on 16 Jul 2022 - 23:13

score 1.5k · Answer 11 · 2026-03-28 10:56:06

1.5k

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Is there a constructive proof of Brouwer's fixed-point theorem that does not rely on triangulation?

Published on 28 Mar 2026 - 10:56

score 289 · Answer 12 · 2026-04-03 02:31:39

289

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Fixed-Point iteration method fails on converging on equation.

Published on 03 Apr 2026 - 2:31

score 247 · Answer 13 · 2022-08-08 15:11:37

247

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Showing that $\mathbf{X}^{2} + \mathbf{X} = \mathbf{A}$ has a solution

Published on 08 Aug 2022 - 15:11

score 41 · Answer 14 · 2026-03-28 03:25:24

41

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Bivariate fixed points

Published on 28 Mar 2026 - 3:25

score 50 · Answer 15 · 2022-08-10 17:00:14

50

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Prove that in a given coloring of a square, there exists a sub-square with a certain coloring.

Published on 10 Aug 2022 - 17:00

List Question

Practice Problems for Revising Basic Results from Analysis

Convergence of Newton's method for Banach spaces

A proof of the sub-super solution method using Schauder's fixed point theorem

If $f\in \mathcal{C}(\mathbb{S}^n,\mathbb{S}^n)$ and $f$ is not surjective, then $f$ has a fixed point

Conditions for $I-x A$ to be a convergent matrix for some $x\in \mathbb{R}$

Cardinality of set $\{f\in C^1 (\mathbb R)\mid f(0)=0,f(2)=2, |f’(x)|\leq 3/2\}$

What are some examples of fixed point problems where transfinite constructions elucidated the problem?

Leray-Schauder Degree for Periodic Functions

If $f\in \mathcal{C}(\mathbb{S}^n,\mathbb{S}^n)$ and $\mathrm{deg}_2(f)=0$, then $f(x_0)=x_0$ and $f(y_0)=-y_0$ for some $x_0, y_0$.

Existence of a fixed point to a vector-valued mapping

Is there a constructive proof of Brouwer's fixed-point theorem that does not rely on triangulation?

Fixed-Point iteration method fails on converging on equation.

Showing that $\mathbf{X}^{2} + \mathbf{X} = \mathbf{A}$ has a solution

Bivariate fixed points

Prove that in a given coloring of a square, there exists a sub-square with a certain coloring.

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