List questions from integral-inequality

Published on 23 Jun 2018 - 11:43

143

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About the proof of the inequality: $\int_0^1 |f(x)|dx\le\text{max}\left(\int_0^1 |f’(x)|dx, \left\vert\int_0^1 f(x)dx\right\vert\right)$

Published on 25 Jun 2018 - 8:55

2.5k

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Mean and root mean square of a random variable

Published on 08 Jul 2018 - 13:12

585

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Gronwall-type inequality with square-root

Published on 11 Jul 2018 - 13:34

62

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Show that $\lim_{t \to \infty} \sup_{x \ge 0} \frac{1}{x^2+1} e^{-x} \sum_{n>t} \frac{n x^{n}}{n!}=0$

Published on 15 Jul 2018 - 17:30

62

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Explanation of why a certain integral-inequality is true

Published on 21 Jul 2018 - 16:23

87

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On solution of a nonlinear differential inequality

Published on 22 Mar 2026 - 17:41

41

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Give a bound of $\|(u_{xx}+u_{yy})\|_p$ by $\|\nabla(\nabla u)\|_p$

Published on 30 Jul 2018 - 17:25

269

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Prove that $\sqrt{\frac{a^2+b^2+c^2+d^2}{4}} \ge \sqrt[3]{\frac{abc+bcd+cda+dab}{4}}$.

Published on 30 Jul 2018 - 19:24

80

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Prove that $\inf\limits_{f\in X}\,I_a(f)=1-a$.

Published on 25 Mar 2026 - 1:17

128

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Upper bound of the integral $\frac{a^{n}}{n!}\int_{0}^{1} e^{at} t^{n}(1-t)^{n}dt$.

Published on 25 Mar 2026 - 1:40

622

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Prove or disprove that integral term is log-concave

Published on 25 Mar 2026 - 3:00

2k

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When is the integral of a square less than the square of the integral?

Published on 06 Aug 2018 - 19:59

88

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Show that $\int_0^\infty 1/f'=\infty.$

Published on 07 Aug 2018 - 5:09

197

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Inequality in natural numbers

Published on 07 Aug 2018 - 15:01

List Question

Bounds for an integral

About the proof of the inequality: $\int_0^1 |f(x)|dx\le\text{max}\left(\int_0^1 |f’(x)|dx, \left\vert\int_0^1 f(x)dx\right\vert\right)$

Mean and root mean square of a random variable

Gronwall-type inequality with square-root

Show that $\lim_{t \to \infty} \sup_{x \ge 0} \frac{1}{x^2+1} e^{-x} \sum_{n>t} \frac{n x^{n}}{n!}=0$

Explanation of why a certain integral-inequality is true

On solution of a nonlinear differential inequality

Give a bound of $\|(u_{xx}+u_{yy})\|_p$ by $\|\nabla(\nabla u)\|_p$

Prove that $\sqrt{\frac{a^2+b^2+c^2+d^2}{4}} \ge \sqrt[3]{\frac{abc+bcd+cda+dab}{4}}$.

Prove that $\inf\limits_{f\in X}\,I_a(f)=1-a$.

Upper bound of the integral $\frac{a^{n}}{n!}\int_{0}^{1} e^{at} t^{n}(1-t)^{n}dt$.

Prove or disprove that integral term is log-concave

When is the integral of a square less than the square of the integral?

Show that $\int_0^\infty 1/f'=\infty.$

Inequality in natural numbers

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