List questions from sequence-of-function

Published on 13 Feb 2020 - 5:21

69

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If $f_n(z)$ converges uniformly to $f(z)$ on a compact set $A\subset\mathbb{c}$ can it be proven $|f_n(z)|$ also converges uniformly to $|f(z)|$?

Published on 14 Feb 2020 - 3:13

48

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$\lim\limits_{k\to\infty} f_1(k)f_2(k)...f_k(k)=\lim\limits_{k\to\infty} f_1(k)\lim\limits_{k\to\infty} f_2(k)...?$

Published on 17 Feb 2020 - 21:35

62

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Pointwise convergence of a series of function.

Published on 18 Feb 2020 - 13:39

195

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Is $P_n[0,1]$ and $P[0,1]$ are closed in $C[0,1]$

Published on 18 Feb 2020 - 15:24

57

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Is $f^{-1} (\alpha) = \bigcap_{m=0}^\infty \bigcup_{n=m+1}^\infty f_n^{-1} (\alpha)$ correct?

Published on 19 Feb 2020 - 23:35

55

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Limit of integral of $\frac{2nx^{n-1}}{1+x},\, x\in [0,1]$

Published on 20 Feb 2020 - 13:15

39

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Find an upperbound as a function of $x$ for $|f_n|$

Published on 23 Feb 2020 - 19:22

144

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Question in solution of a problem whose answer equals to Catalan numbers

Published on 25 Feb 2020 - 7:16

449

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Polynomial Approximation of Holder continuous function

Published on 27 Feb 2020 - 0:02

414

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Dirichlet series - distance between $\sigma_u$ and $\sigma_c$

Published on 27 Feb 2020 - 17:24

955

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Piecewise linear continuous approximation of continuous function

Published on 27 Feb 2020 - 22:12

930

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uniform convergence and convergence of inverse function

Published on 02 Mar 2020 - 14:13

105

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Find the limit function of the given sequence $f_n$.

Published on 05 Mar 2020 - 8:19

45

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About the definition of uniform convergence

Published on 07 Mar 2020 - 21:58

List Question

Sequence of functions and integral multiple choice question

If $f_n(z)$ converges uniformly to $f(z)$ on a compact set $A\subset\mathbb{c}$ can it be proven $|f_n(z)|$ also converges uniformly to $|f(z)|$?

$\lim\limits_{k\to\infty} f_1(k)f_2(k)...f_k(k)=\lim\limits_{k\to\infty} f_1(k)\lim\limits_{k\to\infty} f_2(k)...?$

Pointwise convergence of a series of function.

Is $P_n[0,1]$ and $P[0,1]$ are closed in $C[0,1]$

Is $f^{-1} (\alpha) = \bigcap_{m=0}^\infty \bigcup_{n=m+1}^\infty f_n^{-1} (\alpha)$ correct?

Limit of integral of $\frac{2nx^{n-1}}{1+x},\, x\in [0,1]$

Find an upperbound as a function of $x$ for $|f_n|$

Question in solution of a problem whose answer equals to Catalan numbers

Polynomial Approximation of Holder continuous function

Dirichlet series - distance between $\sigma_u$ and $\sigma_c$

Piecewise linear continuous approximation of continuous function

uniform convergence and convergence of inverse function

Find the limit function of the given sequence $f_n$.

About the definition of uniform convergence

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