List questions from real-analysis

Published on 14 May 2026 - 12:39

244

Views

How to prove that if $F$ belongs to $C^k$ then $F^{-1}$ also belongs to $C^k$?

Published on 16 Apr 2026 - 6:49

385

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proving a mapping is contraction mapping

Published on 10 Apr 2026 - 22:42

84

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Proving some statements, given that $|f(x)-f(y)| \leq M|x-y|^{\alpha}$

Published on 15 May 2026 - 8:45

113

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Proving this log function is continuous

Published on 15 May 2026 - 8:37

323

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Check proof of contraction mapping

Published on 15 Apr 2026 - 2:30

98

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unable to draw regions in ipython notebook

Published on 11 Apr 2026 - 7:53

886

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Proving not contraction mapping

Published on 15 Apr 2026 - 9:41

444

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Finding a domain with $C^1$ boundary

Published on 14 May 2026 - 13:49

439

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Brouwer and Banach fixed point for $x\mapsto f(x)= \frac{e^x}{1+e^x}$

Published on 10 May 2026 - 14:48

773

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Minkowski's triangle inequality for $0<p<1$

Published on 14 Apr 2026 - 7:03

95

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Prove: $1 + \frac12 x - \frac18 x^2 < \sqrt{1+x}, x > 0$

Published on 17 Apr 2026 - 13:40

92

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proof: the sequence $\{x_n\}_{n=1}^{\infty}$ converges, and find $\lim x_n$. (check)

Published on 24 Apr 2026 - 5:20

34

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Covering an interval by a finite number of arbitrary small intervals

Published on 15 Apr 2026 - 9:33

81

Views

prove the convergence of the sequence $z_n$ and $w_n$

Published on 24 Apr 2026 - 6:49

List Question

Proof for inequality involving mean of $k$ closest values

How to prove that if $F$ belongs to $C^k$ then $F^{-1}$ also belongs to $C^k$?

proving a mapping is contraction mapping

Proving some statements, given that $|f(x)-f(y)| \leq M|x-y|^{\alpha}$

Proving this log function is continuous

Check proof of contraction mapping

unable to draw regions in ipython notebook

Proving not contraction mapping

Finding a domain with $C^1$ boundary

Brouwer and Banach fixed point for $x\mapsto f(x)= \frac{e^x}{1+e^x}$

Minkowski's triangle inequality for $0<p<1$

Prove: $1 + \frac12 x - \frac18 x^2 < \sqrt{1+x}, x > 0$

proof: the sequence $\{x_n\}_{n=1}^{\infty}$ converges, and find $\lim x_n$. (check)

Covering an interval by a finite number of arbitrary small intervals

prove the convergence of the sequence $z_n$ and $w_n$

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