Question

Prove inequality $(x^3+2y^3+16\sqrt2)^4 \le 81(x^4+y^4+16)^3$

score 61 · Answer 1 · 2019-07-12 06:05:48

61

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Prove inequality $(x^3+2y^3+16\sqrt2)^4 \le 81(x^4+y^4+16)^3$

Published on 12 Jul 2019 - 6:05

score 51 · Answer 2 · 2019-07-13 12:00:55

51

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Inequality using Hölder $x=\frac{y}{y-1}$ $y>1$

Published on 13 Jul 2019 - 12:00

score 51 · Answer 3 · 2019-07-14 13:50:53

51

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What kind of Hölder inequality is used in the following two estimates

Published on 14 Jul 2019 - 13:50

score 273 · Answer 4 · 2026-03-25 06:13:03

273

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Given three positive numbers $a,b,c$. Prove that $\sum\limits_{cyc}\sqrt{\frac{a+b}{b+1}}\geqq3\sqrt[3]{\frac{4\,abc}{3\,abc+1}}$ .

Published on 25 Mar 2026 - 6:13

score 111 · Answer 5 · 2019-07-20 08:14:20

111

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Let $g$ be a differentiable, continuous function $[0,1]$ and $a≤g'(x)≤b$ for all $x\in [0,1]$

Published on 20 Jul 2019 - 8:14

score 40 · Answer 6 · 2019-07-31 13:44:44

40

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Monotony problem with holder-inequality

Published on 31 Jul 2019 - 13:44

score 35 · Answer 7 · 2019-08-02 07:26:56

35

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Show that $\int_{0}^{1}\left[\frac{I\left(x,n,N-n\right)-I\left(x,n,N-n\right)}{1-2n/N}\right]^{2}dx$ is increasing in $n$?

Published on 02 Aug 2019 - 7:26

score 410 · Answer 8 · 2026-03-25 03:16:36

410

Views

Upper Bound for a Sum

Published on 25 Mar 2026 - 3:16

score 77 · Answer 9 · 2019-08-13 09:33:23

77

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Prove $(x^{3} + x^{4} +y^{3} + y^{4} + z^{3} + z^{4})^{2} \le (x^{6} + y^{6} + z^{6})[ (1+x)^{2} + (1+y)^{2} + (1+z)^{2} ] $

Published on 13 Aug 2019 - 9:33

score 51 · Answer 10 · 2019-08-13 10:14:55

51

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Prove $ (x^{3} + x^{4} +y^{3} + y^{4} + z^{3} + z^{4})^{3} \le (x^{9} + y^{9} + z^{9})[ (1+x)^{3/2} + (1+y)^{3/2} + (1+z)^{3/2} ]^{2} $

Published on 13 Aug 2019 - 10:14

score 107 · Answer 11 · 2019-08-28 05:19:17

107

Views

Proof of equality for Holder's inequality (need verification)

Published on 28 Aug 2019 - 5:19

score 71 · Answer 12 · 2019-09-12 07:51:59

71

Views

The inequality $\lim \frac{1}{2} - \frac{x}{4} + ... + \frac{(-1)^{n} x^{n}}{2^{n+1}} \le \left( \frac{1}{7-7x^{3}} \right)^{1/3}$

Published on 12 Sep 2019 - 7:51

score 103 · Answer 13 · 2019-09-20 10:45:24

103

Views

Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros

Published on 20 Sep 2019 - 10:45

score 164 · Answer 14 · 2019-09-21 04:39:24

Prove Holder inequality by using $a^{\theta}b^{1-\theta}\leq\theta a+(1-\theta)b$ for all $a,b\geq0$ and $\theta\in[0,1]\\$

score 72 · Answer 15 · 2019-09-21 13:01:00

72

Views

Inequality : $\sum_{cyc}\Big(\frac{x^4}{8x^3+5y^3}\Big)^3\geq \frac{x^3+y^3+z^3}{13^3}$

Published on 21 Sep 2019 - 13:01

List Question

Prove inequality $(x^3+2y^3+16\sqrt2)^4 \le 81(x^4+y^4+16)^3$

Inequality using Hölder $x=\frac{y}{y-1}$ $y>1$

What kind of Hölder inequality is used in the following two estimates

Given three positive numbers $a,b,c$. Prove that $\sum\limits_{cyc}\sqrt{\frac{a+b}{b+1}}\geqq3\sqrt[3]{\frac{4\,abc}{3\,abc+1}}$ .

Let $g$ be a differentiable, continuous function $[0,1]$ and $a≤g'(x)≤b$ for all $x\in [0,1]$

Monotony problem with holder-inequality

Show that $\int_{0}^{1}\left[\frac{I\left(x,n,N-n\right)-I\left(x,n,N-n\right)}{1-2n/N}\right]^{2}dx$ is increasing in $n$?

Upper Bound for a Sum

Prove $(x^{3} + x^{4} +y^{3} + y^{4} + z^{3} + z^{4})^{2} \le (x^{6} + y^{6} + z^{6})[ (1+x)^{2} + (1+y)^{2} + (1+z)^{2} ] $

Prove $ (x^{3} + x^{4} +y^{3} + y^{4} + z^{3} + z^{4})^{3} \le (x^{9} + y^{9} + z^{9})[ (1+x)^{3/2} + (1+y)^{3/2} + (1+z)^{3/2} ]^{2} $

Proof of equality for Holder's inequality (need verification)

The inequality $\lim \frac{1}{2} - \frac{x}{4} + ... + \frac{(-1)^{n} x^{n}}{2^{n+1}} \le \left( \frac{1}{7-7x^{3}} \right)^{1/3}$

Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros

Prove Holder inequality by using $a^{\theta}b^{1-\theta}\leq\theta a+(1-\theta)b$ for all $a,b\geq0$ and $\theta\in[0,1]\\$

Inequality : $\sum_{cyc}\Big(\frac{x^4}{8x^3+5y^3}\Big)^3\geq \frac{x^3+y^3+z^3}{13^3}$

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