Question

Prove: $\left(\sqrt{a}+\sqrt{b}+\sqrt{c}\right)^2\ge\sqrt{3}\sum_{cyc}{\sqrt[4]{\frac{5ab}{c}+4a}}$

score 191 · Answer 1 · 2026-03-25 18:50:17

191

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Prove: $\left(\sqrt{a}+\sqrt{b}+\sqrt{c}\right)^2\ge\sqrt{3}\sum_{cyc}{\sqrt[4]{\frac{5ab}{c}+4a}}$

Published on 25 Mar 2026 - 18:50

score 87 · Answer 2 · 2021-10-20 00:58:28

87

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Does Hölder's Inequality implies that $\int_{-\infty}^\infty |f(t) \,g(t)|\,\mathrm dt \leq \int_{-\infty}^\infty |f(t)|\,\mathrm dt \, \sup |g|$?

Published on 20 Oct 2021 - 0:58

score 365 · Answer 3 · 2026-03-23 10:40:49

365

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A generalized version of Hölder's inequality

Published on 23 Mar 2026 - 10:40

score 89 · Answer 4 · 2021-10-30 09:05:26

89

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Prove $\sum_{k=1}^n a_kb_k \leq \left (\sum_{k=1}^n a_k^p \right)^{1/p} \left (\sum_{k=1}^n b_k^{q} \right)^{1/q}$ without Hölder's inequality

Published on 30 Oct 2021 - 9:05

score 77 · Answer 5 · 2021-11-01 04:22:18

77

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Is true $\int\limits_{-\infty}^{\infty} f(t)\,g(t)\,dt \leq \sqrt{\int\limits_{-\infty}^{\infty} |f(t)|^2 dt}\,\cdot \sup\limits_t|g(t)|$?

Published on 01 Nov 2021 - 4:22

score 92 · Answer 6 · 2026-02-24 03:33:04

92

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Is $d(x, y)={(\sum_{i=1}^{n}{|{x_i} -{y_i}|}^p})^{1/p}$ , $x, y\in\mathbb{R^n}$, $0<p<1$ metric on $\mathbb{R^n}$?

Published on 24 Feb 2026 - 3:33

score 27 · Answer 7 · 2021-11-20 12:21:48

27

Views

Is the following estimate of this integral correct?

Published on 20 Nov 2021 - 12:21

score 53 · Answer 8 · 2021-11-25 13:19:56

53

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Scalar Product with Telescope Sum

Published on 25 Nov 2021 - 13:19

score 86 · Answer 9 · 2026-03-26 06:21:10

86

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Two implications of an operator that preserves positivity on L2

Published on 26 Mar 2026 - 6:21

score 280 · Answer 10 · 2021-12-03 23:14:48

280

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Prove Holder's inequality with $0<p<r<q<\infty,\ (1-\theta)/p+\theta/q=1/r$ and $0<\theta<1 \implies \|h\|_r \leq \|h\|_p^{1-\theta} \|h\|_q^{\theta}$

Published on 03 Dec 2021 - 23:14

score 316 · Answer 11 · 2021-12-11 17:11:34

316

Views

Generalization of Cauchy-Schwarz/Hölder inequality

Published on 11 Dec 2021 - 17:11

score 101 · Answer 12 · 2021-12-12 06:19:27

101

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Inequality in cyclic order : $\sum\frac{8}{(a+b)^2+4abc}+a^2+b^2+c^2\ge\sum\frac{8}{a+3}$

Published on 12 Dec 2021 - 6:19

score 50 · Answer 13 · 2021-12-16 13:30:24

50

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Norm with non-negativity constraint

Published on 16 Dec 2021 - 13:30

score 138 · Answer 14 · 2021-12-23 01:24:59

138

Views

How to prove $\|f*g\|_1 \leq \|f\|_1 \cdot \|g\|_1$

Published on 23 Dec 2021 - 1:24

score 28 · Answer 15 · 2021-12-30 01:23:35

28

Views

To show that $\lim_{x\to\infty}\cfrac{1}{x^{1-1/p}}\int_0^x f(t)dt=0$ via Holder's inequality.

Published on 30 Dec 2021 - 1:23

List Question

Prove: $\left(\sqrt{a}+\sqrt{b}+\sqrt{c}\right)^2\ge\sqrt{3}\sum_{cyc}{\sqrt[4]{\frac{5ab}{c}+4a}}$

Does Hölder's Inequality implies that $\int_{-\infty}^\infty |f(t) \,g(t)|\,\mathrm dt \leq \int_{-\infty}^\infty |f(t)|\,\mathrm dt \, \sup |g|$?

A generalized version of Hölder's inequality

Prove $\sum_{k=1}^n a_kb_k \leq \left (\sum_{k=1}^n a_k^p \right)^{1/p} \left (\sum_{k=1}^n b_k^{q} \right)^{1/q}$ without Hölder's inequality

Is true $\int\limits_{-\infty}^{\infty} f(t)\,g(t)\,dt \leq \sqrt{\int\limits_{-\infty}^{\infty} |f(t)|^2 dt}\,\cdot \sup\limits_t|g(t)|$?

Is $d(x, y)={(\sum_{i=1}^{n}{|{x_i} -{y_i}|}^p})^{1/p}$ , $x, y\in\mathbb{R^n}$, $0<p<1$ metric on $\mathbb{R^n}$?

Is the following estimate of this integral correct?

Scalar Product with Telescope Sum

Two implications of an operator that preserves positivity on L2

Prove Holder's inequality with $0<p<r<q<\infty,\ (1-\theta)/p+\theta/q=1/r$ and $0<\theta<1 \implies \|h\|_r \leq \|h\|_p^{1-\theta} \|h\|_q^{\theta}$

Generalization of Cauchy-Schwarz/Hölder inequality

Inequality in cyclic order : $\sum\frac{8}{(a+b)^2+4abc}+a^2+b^2+c^2\ge\sum\frac{8}{a+3}$

Norm with non-negativity constraint

How to prove $\|f*g\|_1 \leq \|f\|_1 \cdot \|g\|_1$

To show that $\lim_{x\to\infty}\cfrac{1}{x^{1-1/p}}\int_0^x f(t)dt=0$ via Holder's inequality.

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