Question

$f_n(x)$ converges uniformly to a function $f(x)$ then does it follow that the limit function $f(x)$ is also uniformly continuous.

score 251 · Answer 1 · 2015-07-19 13:07:00

251

Views

$f_n(x)$ converges uniformly to a function $f(x)$ then does it follow that the limit function $f(x)$ is also uniformly continuous.

Published on 19 Jul 2015 - 13:07

score 166 · Answer 2 · 2015-07-25 08:06:01

166

Views

Convergence that preserves smoothness

Published on 25 Jul 2015 - 8:06

score 411 · Answer 3 · 2015-07-25 21:36:01

411

Views

Pointwise convergence and uniform convergence of $f_n(x) = x^n(1-x)$

Published on 25 Jul 2015 - 21:36

score 116 · Answer 4 · 2026-04-11 05:09:43

116

Views

Does the following series converge uniformly?

Published on 11 Apr 2026 - 5:09

score 211 · Answer 5 · 2015-07-30 06:45:49

211

Views

Does the sequence of functions $f_n(x) = (x + a_n)^2$ converge uniformly?

Published on 30 Jul 2015 - 6:45

score 598 · Answer 6 · 2026-04-09 20:05:30

598

Views

Question on Egoroff-like theorem

Published on 09 Apr 2026 - 20:05

score 72 · Answer 7 · 2015-07-31 12:02:59

72

Views

Does $f_n(x)=\cos^n(x)(1-\cos^n(x))$ converge uniformly for $x$ in $[π/4 , π/2]$?

Published on 31 Jul 2015 - 12:02

score 397 · Answer 8 · 2026-04-10 13:50:40

397

Views

Convergence when the derivative is uniformly continuous

Published on 10 Apr 2026 - 13:50

score 715 · Answer 9 · 2015-07-31 16:15:05

715

Views

When does interchangibility of limit and Riemann integral imply uniform convergence?

Published on 31 Jul 2015 - 16:15

score 237 · Answer 10 · 2015-08-02 14:15:11

237

Views

On the sequence of function $f_n(x)=n^2x(1-x^2)^n $

Published on 02 Aug 2015 - 14:15

score 76 · Answer 11 · 2026-04-10 20:20:31

76

Views

Additional assumptions on function to ensure uniform convergence

Published on 10 Apr 2026 - 20:20

score 1.2k · Answer 12 · 2015-08-04 22:03:08

1.2k

Views

Is the uniform limit of piecewise continuous functions $f:[a,b]\rightarrow\mathbb{R}$ piecewise continuous?

Published on 04 Aug 2015 - 22:03

score 806 · Answer 13 · 2015-08-05 15:49:17

806

Views

Pointwise Convergence to 0 Implies Uniform Convergence to 0

Published on 05 Aug 2015 - 15:49

score 144 · Answer 14 · 2026-04-12 00:32:06

144

Views

Uniform Convergence Proof in Spivak's Calculus

Published on 12 Apr 2026 - 0:32

score 74 · Answer 15 · 2026-04-11 22:02:15

74

Views

Stationary points of a family of functions which converge uniformly.

Published on 11 Apr 2026 - 22:02

List Question

$f_n(x)$ converges uniformly to a function $f(x)$ then does it follow that the limit function $f(x)$ is also uniformly continuous.

Convergence that preserves smoothness

Pointwise convergence and uniform convergence of $f_n(x) = x^n(1-x)$

Does the following series converge uniformly?

Does the sequence of functions $f_n(x) = (x + a_n)^2$ converge uniformly?

Question on Egoroff-like theorem

Does $f_n(x)=\cos^n(x)(1-\cos^n(x))$ converge uniformly for $x$ in $[π/4 , π/2]$?

Convergence when the derivative is uniformly continuous

When does interchangibility of limit and Riemann integral imply uniform convergence?

On the sequence of function $f_n(x)=n^2x(1-x^2)^n $

Additional assumptions on function to ensure uniform convergence

Is the uniform limit of piecewise continuous functions $f:[a,b]\rightarrow\mathbb{R}$ piecewise continuous?

Pointwise Convergence to 0 Implies Uniform Convergence to 0

Uniform Convergence Proof in Spivak's Calculus

Stationary points of a family of functions which converge uniformly.

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