List questions from integral-inequality

Published on 13 Apr 2026 - 22:48

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How to prove $|xe^{-x^2}\int_{0}^{x}e^{t^2}dt-ye^{-y^2}\int_{0}^{y}e^{t^2}dt|<|x-y|$ for $x\ne y$

Published on 16 Apr 2026 - 1:59

289

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How to prove that $\int_{-\pi}^{+\pi}\cos{(2x)}\cos{(3x)}\cos{(4x)}\cdots\cos{(2005x)}dx$ is positive

Published on 15 Apr 2026 - 19:36

261

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an amazing inequality of $L^p$ spaces, how to prove it?

Published on 12 Apr 2026 - 18:41

182

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If $r\leq p\leq s$, prove that $\|f\|_p\leq \max(\|f\|_r,\|f\|_s)$

Published on 17 Apr 2026 - 2:19

507

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How prove this integral inequality $2\int_{-1}^{1}f(x)g(x)dx\ge\int_{-1}^{1}f(x)dx\int_{-1}^{1}g(x)dx$

Published on 17 Apr 2026 - 2:13

4.1k

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Prove Friedrichs' inequality

Published on 15 Apr 2026 - 3:15

105

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Proof about boundedness of $\rm Si$

Published on 13 Apr 2026 - 6:04

70

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An inequality in $L^p$-spaces

Published on 09 Apr 2026 - 1:46

1.4k

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continuity of norms with respect to $p$

Published on 12 Apr 2026 - 12:05

113

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Comparison between two quotients of integrals involving general functions.

Published on 09 Apr 2026 - 21:51

1.8k

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Are integrable, essentially bounded functions in L^p?

Published on 14 May 2026 - 8:56

281

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How prove this integral inequality $\min_{x\in[0,1]}f(x)\ge-\int_{0}^{1}|f'(x)|dx$

Published on 14 Apr 2026 - 16:42

1k

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Maximum value in the Gruss inequality

Published on 14 Apr 2026 - 0:55

1.1k

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Prove that if f(x) is integrable, then so is e^(f(x)).

Published on 15 Apr 2026 - 10:20

List Question

Show that Bellman-Gronwall's inequality

How to prove $|xe^{-x^2}\int_{0}^{x}e^{t^2}dt-ye^{-y^2}\int_{0}^{y}e^{t^2}dt|<|x-y|$ for $x\ne y$

How to prove that $\int_{-\pi}^{+\pi}\cos{(2x)}\cos{(3x)}\cos{(4x)}\cdots\cos{(2005x)}dx$ is positive

an amazing inequality of $L^p$ spaces, how to prove it?

If $r\leq p\leq s$, prove that $\|f\|_p\leq \max(\|f\|_r,\|f\|_s)$

How prove this integral inequality $2\int_{-1}^{1}f(x)g(x)dx\ge\int_{-1}^{1}f(x)dx\int_{-1}^{1}g(x)dx$

Prove Friedrichs' inequality

Proof about boundedness of $\rm Si$

An inequality in $L^p$-spaces

continuity of norms with respect to $p$

Comparison between two quotients of integrals involving general functions.

Are integrable, essentially bounded functions in L^p?

How prove this integral inequality $\min_{x\in[0,1]}f(x)\ge-\int_{0}^{1}|f'(x)|dx$

Maximum value in the Gruss inequality

Prove that if f(x) is integrable, then so is e^(f(x)).

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