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 265 · Answer 1 · 2026-05-07 17:45:32

265

Views

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 07 May 2026 - 17:45

score 136 · Answer 2 · 2026-04-13 18:28:59

136

Views

$L_p$ Norms and Holder's Inequality question

Published on 13 Apr 2026 - 18:28

score 369 · Answer 3 · 2026-04-12 17:41:12

369

Views

Expected value Holder inequality

Published on 12 Apr 2026 - 17:41

score 507 · Answer 4 · 2026-04-15 11:18:13

507

Views

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

Published on 15 Apr 2026 - 11:18

score 639 · Answer 5 · 2026-04-17 11:12:05

639

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 17 Apr 2026 - 11:12

score 284 · Answer 6 · 2026-05-10 14:32:16

284

Views

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 10 May 2026 - 14:32

score 380 · Answer 7 · 2026-05-10 14:40:06

380

Views

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

Published on 10 May 2026 - 14:40

score 103 · Answer 8 · 2026-04-11 07:25:02

103

Views

An application of Holder's Inequality

Published on 11 Apr 2026 - 7:25

score 42 · Answer 9 · 2026-04-16 07:11:24

42

Views

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

Published on 16 Apr 2026 - 7:11

score 102 · Answer 10 · 2026-04-14 22:04:39

102

Views

Hint: Hölder Inequality with $\theta$ application

Published on 14 Apr 2026 - 22:04

score 197 · Answer 11 · 2026-04-18 10:41:01

197

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 18 Apr 2026 - 10:41

score 41 · Answer 12 · 2026-04-11 17:59:30

41

Views

Show that the functional is continuous

Published on 11 Apr 2026 - 17:59

score 95 · Answer 13 · 2026-04-14 23:57:58

95

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 14 Apr 2026 - 23:57

score 133 · Answer 14 · 2026-04-17 07:01:29

133

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 17 Apr 2026 - 7:01

score 882 · Answer 15 · 2026-04-15 05:29:08

882

Views

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

Published on 15 Apr 2026 - 5:29

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 $g$

Trending Questions

Popular # Hahtags

Popular Questions