List questions from holder-inequality

Published on 23 Aug 2020 - 14:16

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Holder's Inequality for integrals (non-negative functions)

Published on 27 Aug 2020 - 8:23

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Hölder's Inequality and $\frac{b}{1/b^\prime} = bb^\prime = \frac{(S_{xy})^2}{S_{xx} S_{yy}}$ get us that $(S_{xy})^2 \le S_{xx} S_{yy}$?

Published on 27 Aug 2020 - 17:27

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Integral version of the Holder Inequality

Published on 29 Aug 2020 - 19:54

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prove that $\sum_{cyc}\frac{a^2}{b}\ge 4$

Published on 02 Sep 2020 - 15:44

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Prove that $\left(x + \sqrt[3]{abc}\right)^3 \le (x + a)(x + b)(x + c) \le \left( x + \frac{a + b + c}{3} \right)^3.$

Published on 03 Sep 2020 - 23:29

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Pseudo Otto Holder proof help.

Published on 07 Sep 2020 - 22:22

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Inequality with a, b, c about finding minimal and maximal value

Published on 10 Sep 2020 - 11:42

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Showing Holder's inequality holds for $p=\infty$ and $q=1$

Published on 11 Sep 2020 - 21:25

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Holder's Inequality application

Published on 15 Sep 2020 - 8:57

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Show that $\int_0^1 f^3(x) dx + \frac{4}{27} \ge \left( \int_0^1 f(x) dx \right)^2$, where $f',f'' >0$

Published on 26 Sep 2020 - 5:02

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Holder inequality of Schatten norm for p=q=2 and Hermitian operators

Published on 27 Sep 2020 - 15:33

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$\frac{a^3}{b+c}+\frac{b^3}{a+c}+\frac{c^3}{a+b}\geq \frac{3}{2}$ for $a,b,c\in\mathbb{R}^+$ with $abc=1$

Published on 26 Mar 2026 - 17:55

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Product of averages

Published on 28 Sep 2020 - 7:48

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For any real positive numbers $a, b, c$, prove that $3(a^2b+b^2c+c^2a)(ab^2+bc^2+ca^2) \geq abc(a+b+c)^3$

Published on 25 Mar 2026 - 19:12

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Inequalities for generalized means

Holder's Inequality for integrals (non-negative functions)

Hölder's Inequality and $\frac{b}{1/b^\prime} = bb^\prime = \frac{(S_{xy})^2}{S_{xx} S_{yy}}$ get us that $(S_{xy})^2 \le S_{xx} S_{yy}$?

Integral version of the Holder Inequality

prove that $\sum_{cyc}\frac{a^2}{b}\ge 4$

Prove that $\left(x + \sqrt[3]{abc}\right)^3 \le (x + a)(x + b)(x + c) \le \left( x + \frac{a + b + c}{3} \right)^3.$

Pseudo Otto Holder proof help.

Inequality with a, b, c about finding minimal and maximal value

Showing Holder's inequality holds for $p=\infty$ and $q=1$

Holder's Inequality application

Show that $\int_0^1 f^3(x) dx + \frac{4}{27} \ge \left( \int_0^1 f(x) dx \right)^2$, where $f',f'' >0$

Holder inequality of Schatten norm for p=q=2 and Hermitian operators

$\frac{a^3}{b+c}+\frac{b^3}{a+c}+\frac{c^3}{a+b}\geq \frac{3}{2}$ for $a,b,c\in\mathbb{R}^+$ with $abc=1$

Product of averages

For any real positive numbers $a, b, c$, prove that $3(a^2b+b^2c+c^2a)(ab^2+bc^2+ca^2) \geq abc(a+b+c)^3$

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