Question

If $a,b$ are positive real numbers, such that $a+b=1$, then prove that $(a+ \dfrac {1}{a})^3 +(b+ \dfrac {1}{b})^3 \ge \dfrac {125}{4}$

score 238 · Answer 1 · 2017-10-28 16:05:21

238

Views

If $a,b$ are positive real numbers, such that $a+b=1$, then prove that $(a+ \dfrac {1}{a})^3 +(b+ \dfrac {1}{b})^3 \ge \dfrac {125}{4}$

Published on 28 Oct 2017 - 16:05

score 1k · Answer 2 · 2017-10-29 15:31:04

1k

Views

Hölder's Inequality in Weak Lebesgue Space

Published on 29 Oct 2017 - 15:31

score 144 · Answer 3 · 2017-10-31 13:26:10

144

Views

Minimum of an expression involving radicals: $\sqrt{\frac{2a}{a+b}} + \sqrt{\frac{2b}{b+c}} + \sqrt{\frac{2c}{c+a}}$

Published on 31 Oct 2017 - 13:26

score 413 · Answer 4 · 2026-03-26 14:20:47

413

Views

Prove that $|a+b|^r\leq 2^{r-1}(|a|^r+|b|^r)$

Published on 26 Mar 2026 - 14:20

score 87 · Answer 5 · 2026-03-25 21:54:05

87

Views

$\Big(\sum\limits_{i=1}^n \frac{1}{x_{i}^2} \Big) \Big(\sum\limits_{i=1}^n \frac{1}{x_{i}^{1/2}}\Big)^{2}$

Published on 25 Mar 2026 - 21:54

score 218 · Answer 6 · 2017-11-03 02:57:11

218

Views

Prove That $ \sqrt{\frac xy + \frac yz}+ \sqrt{\frac yz + \frac zx}+ \sqrt{\frac zx + \frac xy}\ge 3 $

Published on 03 Nov 2017 - 2:57

score 48 · Answer 7 · 2017-11-03 20:42:35

48

Views

Prove $x+y^\alpha z^{1-\alpha}\le (x+y)^\alpha(x+z)^{1-\alpha}$ for $x,y,z\ge 0$ and $0<\alpha<1$

Published on 03 Nov 2017 - 20:42

score 99 · Answer 8 · 2026-03-26 14:18:40

99

Views

Inequality, probably AM-GM inequality

Published on 26 Mar 2026 - 14:18

score 45 · Answer 9 · 2017-11-17 22:00:32

45

Views

Find a function that has finite values for lower norm but becomes infinite

Published on 17 Nov 2017 - 22:00

score 26 · Answer 10 · 2017-11-18 01:46:00

26

Views

Find the lowest value for a lower norm subject to norm-2 being infinite

Published on 18 Nov 2017 - 1:46

score 1.5k · Answer 11 · 2017-11-20 01:45:52

1.5k

Views

Showing a generalized version of the Hölder inequality for $L^{p}$ spaces

Published on 20 Nov 2017 - 1:45

score 304 · Answer 12 · 2017-11-22 12:45:51

304

Views

An inequality by using general Hölder's inequality

Published on 22 Nov 2017 - 12:45

score 2.9k · Answer 13 · 2017-11-25 03:12:13

2.9k

Views

Convolution of L^p and L^q function is uniformly continuous or not?

Published on 25 Nov 2017 - 3:12

score 388 · Answer 14 · 2017-12-08 03:46:32

388

Views

Cauchy Schwarz inequality for surface integrals?

Published on 08 Dec 2017 - 3:46

score 119 · Answer 15 · 2017-12-09 09:25:12

119

Views

Which condition give us equality in Cauchy Schwartz?

Published on 09 Dec 2017 - 9:25

List Question

If $a,b$ are positive real numbers, such that $a+b=1$, then prove that $(a+ \dfrac {1}{a})^3 +(b+ \dfrac {1}{b})^3 \ge \dfrac {125}{4}$

Hölder's Inequality in Weak Lebesgue Space

Minimum of an expression involving radicals: $\sqrt{\frac{2a}{a+b}} + \sqrt{\frac{2b}{b+c}} + \sqrt{\frac{2c}{c+a}}$

Prove that $|a+b|^r\leq 2^{r-1}(|a|^r+|b|^r)$

$\Big(\sum\limits_{i=1}^n \frac{1}{x_{i}^2} \Big) \Big(\sum\limits_{i=1}^n \frac{1}{x_{i}^{1/2}}\Big)^{2}$

Prove That $ \sqrt{\frac xy + \frac yz}+ \sqrt{\frac yz + \frac zx}+ \sqrt{\frac zx + \frac xy}\ge 3 $

Prove $x+y^\alpha z^{1-\alpha}\le (x+y)^\alpha(x+z)^{1-\alpha}$ for $x,y,z\ge 0$ and $0<\alpha<1$

Inequality, probably AM-GM inequality

Find a function that has finite values for lower norm but becomes infinite

Find the lowest value for a lower norm subject to norm-2 being infinite

Showing a generalized version of the Hölder inequality for $L^{p}$ spaces

An inequality by using general Hölder's inequality

Convolution of L^p and L^q function is uniformly continuous or not?

Cauchy Schwarz inequality for surface integrals?

Which condition give us equality in Cauchy Schwartz?

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