Question

If $(f_n')$ converges uniformly on an interval, does $(f_n)$ converge?

score 1.8k · Answer 1 · 2026-04-18 14:55:13

1.8k

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If $(f_n')$ converges uniformly on an interval, does $(f_n)$ converge?

Published on 18 Apr 2026 - 14:55

score 57 · Answer 2 · 2026-04-16 18:57:47

57

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$f_n$ is differentiable on $[a,b]$ and $\lim_{n\to\infty}f_n(x)$ exists for each $x$, Suppose $|f_n'(x)|\leq M$, can we show $f$ is differentiable?

Published on 16 Apr 2026 - 18:57

score 103 · Answer 3 · 2026-04-16 02:46:59

103

Views

Uniform limit theorem and continuity at infinity

Published on 16 Apr 2026 - 2:46

score 127 · Answer 4 · 2026-04-14 05:35:20

127

Views

For what $\alpha$ is the series uniformly convergent on $[0,\infty)$

Published on 14 Apr 2026 - 5:35

score 269 · Answer 5 · 2026-04-17 09:53:49

269

Views

Proving uniform convergence of a Fourier series

Published on 17 Apr 2026 - 9:53

score 109 · Answer 6 · 2026-04-14 17:06:05

109

Views

Bump functions whose derivatives $f^{(n)}(x)$ converge to $0$ uniformly as $n\to\infty$

Published on 14 Apr 2026 - 17:06

score 575 · Answer 7 · 2026-04-17 03:50:20

575

Views

Proving uniform convergence of $\sum_{n=1}^{\infty}a_n\cos{nx}$ in $\mathbb{R}$

Published on 17 Apr 2026 - 3:50

score 44 · Answer 8 · 2026-04-18 20:10:13

44

Views

Showing that a sequence of function does not converge uniformly

Published on 18 Apr 2026 - 20:10

score 145 · Answer 9 · 2026-04-18 14:35:27

145

Views

Why pointwise convergence does not imply uniform convergence?

Published on 18 Apr 2026 - 14:35

score 105 · Answer 10 · 2026-04-14 05:45:34

105

Views

Convergence in distribution of order statistic random variables with uniform distribution.

Published on 14 Apr 2026 - 5:45

score 150 · Answer 11 · 2026-04-13 00:52:33

150

Views

Sequence of holomorphic functions uniformly bounded on compact subsets uniformly converges to $0$ on compact subsets

Published on 13 Apr 2026 - 0:52

score 107 · Answer 12 · 2026-04-14 16:58:06

107

Views

Show that $\sum _{k=1}^{\infty }\frac{\left(-1\right)^kx^k}{k}$ converges uniformly on [0,1]

Published on 14 Apr 2026 - 16:58

score 45 · Answer 13 · 2026-04-18 14:29:19

45

Views

misconception about pointwise/uniform convergence

Published on 18 Apr 2026 - 14:29

score 62 · Answer 14 · 2026-04-16 07:39:10

62

Views

Uniform convergence on $X \times X$.

Published on 16 Apr 2026 - 7:39

score 29 · Answer 15 · 2026-04-18 20:14:32

29

Views

Convergence of a sequence of functions to uniformly continuous function

Published on 18 Apr 2026 - 20:14

List Question

If $(f_n')$ converges uniformly on an interval, does $(f_n)$ converge?

$f_n$ is differentiable on $[a,b]$ and $\lim_{n\to\infty}f_n(x)$ exists for each $x$, Suppose $|f_n'(x)|\leq M$, can we show $f$ is differentiable?

Uniform limit theorem and continuity at infinity

For what $\alpha$ is the series uniformly convergent on $[0,\infty)$

Proving uniform convergence of a Fourier series

Bump functions whose derivatives $f^{(n)}(x)$ converge to $0$ uniformly as $n\to\infty$

Proving uniform convergence of $\sum_{n=1}^{\infty}a_n\cos{nx}$ in $\mathbb{R}$

Showing that a sequence of function does not converge uniformly

Why pointwise convergence does not imply uniform convergence?

Convergence in distribution of order statistic random variables with uniform distribution.

Sequence of holomorphic functions uniformly bounded on compact subsets uniformly converges to $0$ on compact subsets

Show that $\sum _{k=1}^{\infty }\frac{\left(-1\right)^kx^k}{k}$ converges uniformly on [0,1]

misconception about pointwise/uniform convergence

Uniform convergence on $X \times X$.

Convergence of a sequence of functions to uniformly continuous function

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