Question

Find the minimum value of $P=\left(3+\frac{1}{a}+\frac{1}{b}\right)\left(3+\frac{1}{b}+\frac{1}{c}\right)\left(3+\frac{1}{c}+\frac{1}{a}\right)$

score 150 · Answer 1 · 2017-03-27 14:26:57

150

Views

Find the minimum value of $P=\left(3+\frac{1}{a}+\frac{1}{b}\right)\left(3+\frac{1}{b}+\frac{1}{c}\right)\left(3+\frac{1}{c}+\frac{1}{a}\right)$

Published on 27 Mar 2017 - 14:26

score 3.2k · Answer 2 · 2017-04-09 07:15:51

3.2k

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Prove that $\frac{1}{a^3(b+c)} + \frac{1}{b^3(a+c)} + \frac{1}{c^3(a+b)} \geq \frac{3}{2} \text{ when } abc=1$

Published on 09 Apr 2017 - 7:15

score 104 · Answer 3 · 2026-03-25 08:13:38

104

Views

About functions in fractional Sobolev spaces $W^{s,p}(\mathbb{R})$ and $\lim_{x\rightarrow a^{+}}\int_{a}^{x}\frac{f(y)}{(x-y)^{s}}dy=0$

Published on 25 Mar 2026 - 8:13

score 28 · Answer 4 · 2026-03-25 06:12:40

28

Views

Are there any refinements of $\langle \vec x,\vec y\rangle \leq \lVert \vec x\rVert_1\lVert \vec y\rVert_\infty$?

Published on 25 Mar 2026 - 6:12

score 78 · Answer 5 · 2023-02-01 16:19:03

78

Views

show inequality with Hölder or induction?

Published on 01 Feb 2023 - 16:19

score 66 · Answer 6 · 2023-02-04 19:39:38

66

Views

relationship between generalized mean ratios $M_4(a)/M_2(a)$ vs $M_2(a)/M_1(a)$

Published on 04 Feb 2023 - 19:39

score 58 · Answer 7 · 2023-02-04 22:42:22

58

Views

Bounding growth of generalised mean $M_p(a)$ as $p$ increases

Published on 04 Feb 2023 - 22:42

score 102 · Answer 8 · 2026-03-22 14:28:57

102

Views

Pulling out a maximum term from an integral

Published on 22 Mar 2026 - 14:28

score 114 · Answer 9 · 2023-02-11 21:04:20

114

Views

I want to prove for all $a > 0 $, $b > 0$, $\frac{2ab}{a + b} + \sqrt{\frac{1}{2}\left(a^2 + b^2\right)} \geq \frac{a + b}{2} + \sqrt{ab}$

Published on 11 Feb 2023 - 21:04

score 169 · Answer 10 · 2026-03-25 12:54:41

169

Views

Does the $\log$-$\exp$ analogous of Minkowski integral inequality hold true?

Published on 25 Mar 2026 - 12:54

score 116 · Answer 11 · 2023-03-03 02:36:33

116

Views

How to use Hölder inequality to prove this integral inequality?

Published on 03 Mar 2023 - 2:36

score 213 · Answer 12 · 2023-03-08 00:38:50

213

Views

Holder's Inequality for p < 0 or q < 0

Published on 08 Mar 2023 - 0:38

score 156 · Answer 13 · 2026-03-25 06:10:15

156

Views

Young's inequality in probability theory

Published on 25 Mar 2026 - 6:10

score 66 · Answer 14 · 2023-03-23 01:56:52

66

Views

Applying Holder Inequality to obtain a estimate.

Published on 23 Mar 2023 - 1:56

score 139 · Answer 15 · 2023-03-23 20:11:13

139

Views

Prove $\sum\limits_{\mathrm{cyc}}\frac{{{a^3}}}{{\sqrt {{b^2} + {c^2}} }} \ge \frac{1}{{\sqrt {2(ab + bc + ca)} }}$ for $a^2+b^2+c^2=1$

Published on 23 Mar 2023 - 20:11

List Question

Find the minimum value of $P=\left(3+\frac{1}{a}+\frac{1}{b}\right)\left(3+\frac{1}{b}+\frac{1}{c}\right)\left(3+\frac{1}{c}+\frac{1}{a}\right)$

Prove that $\frac{1}{a^3(b+c)} + \frac{1}{b^3(a+c)} + \frac{1}{c^3(a+b)} \geq \frac{3}{2} \text{ when } abc=1$

About functions in fractional Sobolev spaces $W^{s,p}(\mathbb{R})$ and $\lim_{x\rightarrow a^{+}}\int_{a}^{x}\frac{f(y)}{(x-y)^{s}}dy=0$

Are there any refinements of $\langle \vec x,\vec y\rangle \leq \lVert \vec x\rVert_1\lVert \vec y\rVert_\infty$?

show inequality with Hölder or induction?

relationship between generalized mean ratios $M_4(a)/M_2(a)$ vs $M_2(a)/M_1(a)$

Bounding growth of generalised mean $M_p(a)$ as $p$ increases

Pulling out a maximum term from an integral

I want to prove for all $a > 0 $, $b > 0$, $\frac{2ab}{a + b} + \sqrt{\frac{1}{2}\left(a^2 + b^2\right)} \geq \frac{a + b}{2} + \sqrt{ab}$

Does the $\log$-$\exp$ analogous of Minkowski integral inequality hold true?

How to use Hölder inequality to prove this integral inequality?

Holder's Inequality for p < 0 or q < 0

Young's inequality in probability theory

Applying Holder Inequality to obtain a estimate.

Prove $\sum\limits_{\mathrm{cyc}}\frac{{{a^3}}}{{\sqrt {{b^2} + {c^2}} }} \ge \frac{1}{{\sqrt {2(ab + bc + ca)} }}$ for $a^2+b^2+c^2=1$

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