Question

Finding counterexamples to prove: $f_n \to f$ uniformly on $(0,\infty)$ does not imply $1/f_n \to 1/f$ uniformly on $(0,\infty)$

score 44 · Answer 1 · 2026-04-15 02:35:58

44

Views

Finding counterexamples to prove: $f_n \to f$ uniformly on $(0,\infty)$ does not imply $1/f_n \to 1/f$ uniformly on $(0,\infty)$

Published on 15 Apr 2026 - 2:35

score 127 · Answer 2 · 2026-04-16 04:44:16

127

Views

Uniform Convergence of Taylor Remainder

Published on 16 Apr 2026 - 4:44

score 65 · Answer 3 · 2026-04-17 06:10:57

65

Views

Convergence of sequence of functions with supremum metric

Published on 17 Apr 2026 - 6:10

score 240 · Answer 4 · 2026-04-12 00:06:07

240

Views

showing the power series $\sum_{n=1}^{\infty} \frac{z^n}{n^2}$ is holomorphic in the open unit disk but not closed

Published on 12 Apr 2026 - 0:06

score 158 · Answer 5 · 2026-04-16 21:18:51

158

Views

$g_{n}(x):=max \lbrace f_{1}(x),....\rbrace$ uniformly convergent if $\lbrace f_{n} \rbrace_{n \in \mathbb{N}}$ uniformly bounded and equicontinuous

Published on 16 Apr 2026 - 21:18

score 65 · Answer 6 · 2026-04-14 23:44:03

65

Views

Uniform convergence in finite dimensional subspace of $C[0,1]$.

Published on 14 Apr 2026 - 23:44

score 75 · Answer 7 · 2026-04-17 06:10:57

75

Views

convergence of series of sinus functions

Published on 17 Apr 2026 - 6:10

score 85 · Answer 8 · 2026-04-14 15:28:42

85

Views

Prove uniform convergence for piecewise function

Published on 14 Apr 2026 - 15:28

score 120 · Answer 9 · 2026-04-16 03:47:21

120

Views

Is the map $f(x)=x+\cfrac{1}{4}\sin^2(\pi x)$ uniquely ergodic?

Published on 16 Apr 2026 - 3:47

score 341 · Answer 10 · 2026-04-16 16:20:37

341

Views

$f_n(x) = \frac{x}{n^2} e^{-\frac{x}{n}}$ converges uniformly to zero

Published on 16 Apr 2026 - 16:20

score 113 · Answer 11 · 2026-04-17 13:51:37

113

Views

$f_n(x) = (n+1)x^n(1-x)$, on which interval does $f_n$ converge uniformly?

Published on 17 Apr 2026 - 13:51

score 126 · Answer 12 · 2026-04-20 06:51:29

126

Views

Find the pointwise limit of the sequence$f_n(x) = {1\over 1+x} + {2\over 1+x^2} + {4\over 1+x^4}+...+{2^n\over 1+x^{2^n}}$

Published on 20 Apr 2026 - 6:51

score 57 · Answer 13 · 2026-04-15 07:59:47

57

Views

Topology of uniform convergence of functions $X\to X$?

Published on 15 Apr 2026 - 7:59

score 81 · Answer 14 · 2026-04-12 22:50:55

81

Views

Seeking for a counterexample where the convergence of the series of derivatives isn't uniform

Published on 12 Apr 2026 - 22:50

score 34 · Answer 15 · 2026-04-13 00:07:44

34

Views

Some doubts on uniform convergence

Published on 13 Apr 2026 - 0:07

List Question

Finding counterexamples to prove: $f_n \to f$ uniformly on $(0,\infty)$ does not imply $1/f_n \to 1/f$ uniformly on $(0,\infty)$

Uniform Convergence of Taylor Remainder

Convergence of sequence of functions with supremum metric

showing the power series $\sum_{n=1}^{\infty} \frac{z^n}{n^2}$ is holomorphic in the open unit disk but not closed

$g_{n}(x):=max \lbrace f_{1}(x),....\rbrace$ uniformly convergent if $\lbrace f_{n} \rbrace_{n \in \mathbb{N}}$ uniformly bounded and equicontinuous

Uniform convergence in finite dimensional subspace of $C[0,1]$.

convergence of series of sinus functions

Prove uniform convergence for piecewise function

Is the map $f(x)=x+\cfrac{1}{4}\sin^2(\pi x)$ uniquely ergodic?

$f_n(x) = \frac{x}{n^2} e^{-\frac{x}{n}}$ converges uniformly to zero

$f_n(x) = (n+1)x^n(1-x)$, on which interval does $f_n$ converge uniformly?

Find the pointwise limit of the sequence$f_n(x) = {1\over 1+x} + {2\over 1+x^2} + {4\over 1+x^4}+...+{2^n\over 1+x^{2^n}}$

Topology of uniform convergence of functions $X\to X$?

Seeking for a counterexample where the convergence of the series of derivatives isn't uniform

Some doubts on uniform convergence

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