Question

Sequence $(f_n) \to f_n$ on $S \subseteq \mathbb{R}$ converges uniformly iff $\lim_{n \to \infty} \sup \{f(x)-f_n(x)| : x\in S\} = 0$

score 109 · Answer 1 · 2026-05-11 09:15:27

109

Views

Sequence $(f_n) \to f_n$ on $S \subseteq \mathbb{R}$ converges uniformly iff $\lim_{n \to \infty} \sup \{f(x)-f_n(x)| : x\in S\} = 0$

Published on 11 May 2026 - 9:15

score 90 · Answer 2 · 2026-04-13 00:03:35

90

Views

Sequence of bounded sequences converge uniformly to bounded function

Published on 13 Apr 2026 - 0:03

score 39 · Answer 3 · 2026-05-10 16:06:35

39

Views

What is the rate of convergence of the argmins of a sequence of uniformly convergent strictly convex functions?

Published on 10 May 2026 - 16:06

score 587 · Answer 4 · 2026-04-14 20:39:22

587

Views

Question on uniform convergence of sum of continuous functions.

Published on 14 Apr 2026 - 20:39

score 329 · Answer 5 · 2026-05-11 09:15:11

329

Views

If $\sum g_n(x)$ converges uniformly and absolutely and $|f_n(x)|\leq |g_n(x)|$ show that $\sum f_n(x)$ converges uniformly and absolutely.

Published on 11 May 2026 - 9:15

score 76 · Answer 6 · 2026-04-14 04:11:11

76

Views

Determine pointwise and uniform convergence of a given sequence of functions and calculate an integral

Published on 14 Apr 2026 - 4:11

score 57 · Answer 7 · 2026-05-15 03:03:05

57

Views

if $f_n(z)\rightarrow f(z)$ uniformly, then $ \frac{f'_n(z)}{f_n(z)}\rightarrow\frac{f'(z)}{f(z)}$ uniformly?

Published on 15 May 2026 - 3:03

score 90 · Answer 8 · 2026-04-16 04:45:52

90

Views

Is $\lim_{n\to\infty}\int_0^1f_n(x)=\int_0^1f(x)$ in this case?

Published on 16 Apr 2026 - 4:45

score 40 · Answer 9 · 2026-04-16 14:50:23

40

Views

Convergence of sequence $f'_n(x)$

Published on 16 Apr 2026 - 14:50

score 30 · Answer 10 · 2026-04-17 13:46:03

30

Views

Prove that the sequence of derivative functions converges uniformly on every interval [-M,M].

Published on 17 Apr 2026 - 13:46

score 74 · Answer 11 · 2026-05-06 23:05:23

74

Views

Uniformly approximating $f\in \mathcal{C}([1,\infty))$ with polynomials where $\underset{x\rightarrow +\infty}{\lim} f(x)=a$

Published on 06 May 2026 - 23:05

score 37 · Answer 12 · 2026-04-13 21:17:59

37

Views

Establish uniform convergence

Published on 13 Apr 2026 - 21:17

score 67 · Answer 13 · 2026-04-12 06:59:20

67

Views

Is it true that $f(x) = x^{2}$ is uniformly continuous on $\mathbb{N}$?

Published on 12 Apr 2026 - 6:59

score 238 · Answer 14 · 2026-04-13 01:14:35

238

Views

Using the sequential definition of uniform continuity to show $\sin(x)$ is uniformly continuous on $\mathbb{R}$

Published on 13 Apr 2026 - 1:14

score 465 · Answer 15 · 2026-05-14 05:17:27

465

Views

Showing that the almost uniform limit of functions with bounded $L_\infty$ norms is in $L_\infty$

Published on 14 May 2026 - 5:17

List Question

Sequence $(f_n) \to f_n$ on $S \subseteq \mathbb{R}$ converges uniformly iff $\lim_{n \to \infty} \sup \{f(x)-f_n(x)| : x\in S\} = 0$

Sequence of bounded sequences converge uniformly to bounded function

What is the rate of convergence of the argmins of a sequence of uniformly convergent strictly convex functions?

Question on uniform convergence of sum of continuous functions.

If $\sum g_n(x)$ converges uniformly and absolutely and $|f_n(x)|\leq |g_n(x)|$ show that $\sum f_n(x)$ converges uniformly and absolutely.

Determine pointwise and uniform convergence of a given sequence of functions and calculate an integral

if $f_n(z)\rightarrow f(z)$ uniformly, then $ \frac{f'_n(z)}{f_n(z)}\rightarrow\frac{f'(z)}{f(z)}$ uniformly?

Is $\lim_{n\to\infty}\int_0^1f_n(x)=\int_0^1f(x)$ in this case?

Convergence of sequence $f'_n(x)$

Prove that the sequence of derivative functions converges uniformly on every interval [-M,M].

Uniformly approximating $f\in \mathcal{C}([1,\infty))$ with polynomials where $\underset{x\rightarrow +\infty}{\lim} f(x)=a$

Establish uniform convergence

Is it true that $f(x) = x^{2}$ is uniformly continuous on $\mathbb{N}$?

Using the sequential definition of uniform continuity to show $\sin(x)$ is uniformly continuous on $\mathbb{R}$

Showing that the almost uniform limit of functions with bounded $L_\infty$ norms is in $L_\infty$

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