Question

Proving $\sum\limits_{\text{cyc}} \frac{a}{b^2+c^2+d^2} \geq \frac{3\sqrt{3}}{2}\frac{1}{\sqrt{a^2+b^2+c^2+d^2}}$ for $a, b, c, d >0$

score 257 · Answer 1 · 2026-03-19 22:28:43

257

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Proving $\sum\limits_{\text{cyc}} \frac{a}{b^2+c^2+d^2} \geq \frac{3\sqrt{3}}{2}\frac{1}{\sqrt{a^2+b^2+c^2+d^2}}$ for $a, b, c, d >0$

Published on 19 Mar 2026 - 22:28

score 133 · Answer 2 · 2018-11-02 07:22:04

133

Views

$L_p$ Norms and Holder's Inequality question

Published on 02 Nov 2018 - 7:22

score 365 · Answer 3 · 2018-11-05 14:43:48

365

Views

Expected value Holder inequality

Published on 05 Nov 2018 - 14:43

score 504 · Answer 4 · 2018-11-08 20:24:55

504

Views

Showing a product of two Lebesgue integrals is $\geq 1$ if the product of the integrands is $\geq 1$

Published on 08 Nov 2018 - 20:24

score 636 · Answer 5 · 2018-11-09 12:41:37

636

Views

$\frac{a}{\sqrt{a^2 + 8bc}} +\frac{b}{\sqrt{b^2 + 8ac}} + \frac{c}{\sqrt{c^2 + 8ab}} \ge \frac{1}{\sqrt{a^3+b^3+c^3 + 24abc}}$ is true?

Published on 09 Nov 2018 - 12:41

score 283 · Answer 6 · 2026-03-25 01:18:32

283

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If $a$, $b$, $c$ are positive real numbers such that $a^2 + b^2 + c^2 = 27$. Find the least value of $a^3 + b^3 + c^3$?

Published on 25 Mar 2026 - 1:18

score 378 · Answer 7 · 2018-12-04 16:51:16

378

Views

Prove that $({a\over a+b})^3+({b\over b+c})^3+ ({c\over c+a})^3\geq {3\over 8}$

Published on 04 Dec 2018 - 16:51

score 99 · Answer 8 · 2018-12-04 19:54:20

99

Views

An application of Holder's Inequality

Published on 04 Dec 2018 - 19:54

score 39 · Answer 9 · 2018-12-06 17:29:17

39

Views

Showing $f:=f_{1},...,f_{n}\in L^{p}(\mu)$ for $f_{i} \in L^{p_{i}}$

Published on 06 Dec 2018 - 17:29

score 99 · Answer 10 · 2018-12-06 19:55:02

99

Views

Hint: Hölder Inequality with $\theta$ application

Published on 06 Dec 2018 - 19:55

score 194 · Answer 11 · 2018-12-08 07:54:47

194

Views

Find the minimum value of $\sqrt {2x^2+2y^2} +\sqrt {y^2+x^2-4y+4} +\sqrt {x^2+y^2-4x-4y+8}$

Published on 08 Dec 2018 - 7:54

score 38 · Answer 12 · 2018-12-11 17:57:35

38

Views

Show that the functional is continuous

Published on 11 Dec 2018 - 17:57

score 93 · Answer 13 · 2018-12-12 14:27:00

93

Views

A simple proof for $\prod_{i=1}^d a_i+\prod_{i=1}^d b_i \le \prod_{i=1}^d (a_i^d+b_i^d)^{1/d}$?

Published on 12 Dec 2018 - 14:27

score 130 · Answer 14 · 2018-12-14 06:22:31

130

Views

Let $T(f)(y)=\int_0^\infty K(x,y)\cdot f(x)dx$, $\,$ show $\,$ $\Vert T(f) \Vert _p \le C\cdot \Vert f \Vert _p$

Published on 14 Dec 2018 - 6:22

score 879 · Answer 15 · 2018-12-18 23:12:38

879

Views

The Convergence of Convolution of $f$ and $g$

Published on 18 Dec 2018 - 23:12

List Question

Proving $\sum\limits_{\text{cyc}} \frac{a}{b^2+c^2+d^2} \geq \frac{3\sqrt{3}}{2}\frac{1}{\sqrt{a^2+b^2+c^2+d^2}}$ for $a, b, c, d >0$

$L_p$ Norms and Holder's Inequality question

Expected value Holder inequality

Showing a product of two Lebesgue integrals is $\geq 1$ if the product of the integrands is $\geq 1$

$\frac{a}{\sqrt{a^2 + 8bc}} +\frac{b}{\sqrt{b^2 + 8ac}} + \frac{c}{\sqrt{c^2 + 8ab}} \ge \frac{1}{\sqrt{a^3+b^3+c^3 + 24abc}}$ is true?

If $a$, $b$, $c$ are positive real numbers such that $a^2 + b^2 + c^2 = 27$. Find the least value of $a^3 + b^3 + c^3$?

Prove that $({a\over a+b})^3+({b\over b+c})^3+ ({c\over c+a})^3\geq {3\over 8}$

An application of Holder's Inequality

Showing $f:=f_{1},...,f_{n}\in L^{p}(\mu)$ for $f_{i} \in L^{p_{i}}$

Hint: Hölder Inequality with $\theta$ application

Find the minimum value of $\sqrt {2x^2+2y^2} +\sqrt {y^2+x^2-4y+4} +\sqrt {x^2+y^2-4x-4y+8}$

Show that the functional is continuous

A simple proof for $\prod_{i=1}^d a_i+\prod_{i=1}^d b_i \le \prod_{i=1}^d (a_i^d+b_i^d)^{1/d}$?

Let $T(f)(y)=\int_0^\infty K(x,y)\cdot f(x)dx$, $\,$ show $\,$ $\Vert T(f) \Vert _p \le C\cdot \Vert f \Vert _p$

The Convergence of Convolution of $f$ and $g$

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