Question

Uniform convergence of function series with parameter.

score 55 · Answer 1 · 2026-04-12 14:06:41

55

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Uniform convergence of function series with parameter.

Published on 12 Apr 2026 - 14:06

score 59 · Answer 2 · 2026-04-13 17:43:39

59

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Convergence of sequence of convex functions and its first derivative

Published on 13 Apr 2026 - 17:43

score 37 · Answer 3 · 2026-04-17 02:27:57

37

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$(L_{c}(E,F),\left \| . \right \|_{E\rightarrow F})$ Banach $\Leftrightarrow (F,\left \| . \right \|_{F})$ Banach

Published on 17 Apr 2026 - 2:27

score 184 · Answer 4 · 2026-04-22 06:54:24

184

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On Bartle's 'Elements of Integration' Exercise 7.U

Published on 22 Apr 2026 - 6:54

score 111 · Answer 5 · 2026-04-16 11:15:42

111

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When can a double limit $\lim_{k\to\infty}\lim_{m\to\infty}f_{k,m}(x)$ be combined into $\lim_{k\to\infty}f_{k,k}(x)$?

Published on 16 Apr 2026 - 11:15

score 76 · Answer 6 · 2026-04-21 16:15:31

76

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Is converge pointwise with this property implies uniform convergence?

Published on 21 Apr 2026 - 16:15

score 48 · Answer 7 · 2026-04-21 16:22:26

48

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Spivak, Ch. 24, Problem 1a: Does $\sqrt[n]{x}$ converge pointwise to $f(x)=1, x\in (0,1]$, $f(0)=0$ on $(0,1]$ or on $[0,1]$?

Published on 21 Apr 2026 - 16:22

score 57 · Answer 8 · 2026-04-16 21:19:20

57

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Spivak, Ch. 24, Problem 2(iii): Proving uniform convergence of sequence of functions $f_n(x)=\sqrt{x^2+\frac{1}{n^2}}$.

Published on 16 Apr 2026 - 21:19

score 93 · Answer 9 · 2026-04-14 17:42:00

93

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Uniform convergence of this series

Published on 14 Apr 2026 - 17:42

score 65 · Answer 10 · 2026-04-15 20:09:06

65

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Spivak, Ch. 24, "Uniform Convergence and Power Series": Understanding statement of Theorem 6

Published on 15 Apr 2026 - 20:09

score 69 · Answer 11 · 2026-04-16 04:08:02

69

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Show $ \sum_{k=1}^\infty (-1)^{k} x^{\sqrt{2}+k }$ converges uniformly on $[0,b]$ for $b$ less than 1

Published on 16 Apr 2026 - 4:08

score 111 · Answer 12 · 2026-04-17 15:29:43

111

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How do we justify the integration of $f'(x)=\arcsin'{(x)}=\frac{1}{\sqrt{1-x^2}}=\sum\limits_{k=0}^\infty \binom{-1/2}{k}x^{2k}$?

Published on 17 Apr 2026 - 15:29

score 121 · Answer 13 · 2026-04-14 10:19:35

121

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How can we prove the uniform convergence of an integrand, without using the dominated convergence theorem?

Published on 14 Apr 2026 - 10:19

score 107 · Answer 14 · 2026-04-22 06:56:37

107

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Converse of the Weierstrass M-Test

Published on 22 Apr 2026 - 6:56

score 44 · Answer 15 · 2026-04-17 12:38:39

44

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uniform convergence of $f_n(x) = \frac{nx}{1+n^2x^2}$

Published on 17 Apr 2026 - 12:38

List Question

Uniform convergence of function series with parameter.

Convergence of sequence of convex functions and its first derivative

$(L_{c}(E,F),\left \| . \right \|_{E\rightarrow F})$ Banach $\Leftrightarrow (F,\left \| . \right \|_{F})$ Banach

On Bartle's 'Elements of Integration' Exercise 7.U

When can a double limit $\lim_{k\to\infty}\lim_{m\to\infty}f_{k,m}(x)$ be combined into $\lim_{k\to\infty}f_{k,k}(x)$?

Is converge pointwise with this property implies uniform convergence?

Spivak, Ch. 24, Problem 1a: Does $\sqrt[n]{x}$ converge pointwise to $f(x)=1, x\in (0,1]$, $f(0)=0$ on $(0,1]$ or on $[0,1]$?

Spivak, Ch. 24, Problem 2(iii): Proving uniform convergence of sequence of functions $f_n(x)=\sqrt{x^2+\frac{1}{n^2}}$.

Uniform convergence of this series

Spivak, Ch. 24, "Uniform Convergence and Power Series": Understanding statement of Theorem 6

Show $ \sum_{k=1}^\infty (-1)^{k} x^{\sqrt{2}+k }$ converges uniformly on $[0,b]$ for $b$ less than 1

How do we justify the integration of $f'(x)=\arcsin'{(x)}=\frac{1}{\sqrt{1-x^2}}=\sum\limits_{k=0}^\infty \binom{-1/2}{k}x^{2k}$?

How can we prove the uniform convergence of an integrand, without using the dominated convergence theorem?

Converse of the Weierstrass M-Test

uniform convergence of $f_n(x) = \frac{nx}{1+n^2x^2}$

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