Question

The other side of Jensen's inequality

score 161 · Answer 1 · 2020-08-07 22:58:26

161

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The other side of Jensen's inequality

Published on 07 Aug 2020 - 22:58

score 321 · Answer 2 · 2020-08-14 03:46:59

321

Views

Proof that if $x,y>0$ and $x+y=1$, then $(2x)^{\frac 1 x}+(2y)^{\frac 1 y}\leq 2$

Published on 14 Aug 2020 - 3:46

score 795 · Answer 3 · 2020-08-14 05:27:02

795

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Proving $\int_{0}^{1}xf(x)dx \leq \frac{2}{3}\int_{0}^{1}f(x)dx$ for all concave functions $f: [0,1]\rightarrow [0,\infty)$

Published on 14 Aug 2020 - 5:27

score 277 · Answer 4 · 2020-08-16 21:13:54

277

Views

Probability inequality for sum of non-negative independent random variables

Published on 16 Aug 2020 - 21:13

score 93 · Answer 5 · 2020-08-21 18:51:46

93

Views

Using Jensen's Inequality to show a given function is square integrable

Published on 21 Aug 2020 - 18:51

score 147 · Answer 6 · 2020-08-27 04:57:47

147

Views

Is the infimum $\int_{X} F(g)$ over all $g$ such that $ \int_X g=c $ obtained?

Published on 27 Aug 2020 - 4:57

score 286 · Answer 7 · 2020-08-30 00:17:55

286

Views

Show $(\sum | a_i - b_i |)^2 \leq (\sum ( \sqrt{a_i} - \sqrt{b_i} )^2 ) (\sum ( \sqrt{a_i} + \sqrt{b_i} )^2 )$

Published on 30 Aug 2020 - 0:17

score 312 · Answer 8 · 2020-09-01 22:12:51

312

Views

Proving Jensen's Inequality for Arbitrary Intervals

Published on 01 Sep 2020 - 22:12

score 2.9k · Answer 9 · 2020-09-10 14:41:57

2.9k

Views

sum of log versus log of sum

Published on 10 Sep 2020 - 14:41

score 63 · Answer 10 · 2020-09-18 03:54:53

63

Views

$(1+x)^d \leq 1 + x^d$ for $x \geq 0$ and $d \in (0,1]$

Published on 18 Sep 2020 - 3:54

score 107 · Answer 11 · 2020-09-18 05:15:41

107

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Show that: $ x_{1}^n + x_{2}^n + · · · + x_{n}^n ≥ nx_{1} x_{2} · · · x_{n} $.

Published on 18 Sep 2020 - 5:15

score 270 · Answer 12 · 2020-09-21 17:43:37

270

Views

Showing the inequality $f(x)=x^{2(1-x)}+(1-x)^{2x}\leq 1$ for $0<x<1$

Published on 21 Sep 2020 - 17:43

score 45 · Answer 13 · 2020-09-22 16:37:18

45

Views

Random variable in $L^p$ implies random variable in $L^1$

Published on 22 Sep 2020 - 16:37

score 128 · Answer 14 · 2020-09-25 16:28:50

128

Views

Finding bounds for the absolute value of function raised to positive constant

Published on 25 Sep 2020 - 16:28

score 68 · Answer 15 · 2020-09-27 21:38:27

68

Views

Undertanding Jensen's inequality proof on countable basis Hilbert with Radon measure

Published on 27 Sep 2020 - 21:38

List Question

The other side of Jensen's inequality

Proof that if $x,y>0$ and $x+y=1$, then $(2x)^{\frac 1 x}+(2y)^{\frac 1 y}\leq 2$

Proving $\int_{0}^{1}xf(x)dx \leq \frac{2}{3}\int_{0}^{1}f(x)dx$ for all concave functions $f: [0,1]\rightarrow [0,\infty)$

Probability inequality for sum of non-negative independent random variables

Using Jensen's Inequality to show a given function is square integrable

Is the infimum $\int_{X} F(g)$ over all $g$ such that $ \int_X g=c $ obtained?

Show $(\sum | a_i - b_i |)^2 \leq (\sum ( \sqrt{a_i} - \sqrt{b_i} )^2 ) (\sum ( \sqrt{a_i} + \sqrt{b_i} )^2 )$

Proving Jensen's Inequality for Arbitrary Intervals

sum of log versus log of sum

$(1+x)^d \leq 1 + x^d$ for $x \geq 0$ and $d \in (0,1]$

Show that: $ x_{1}^n + x_{2}^n + · · · + x_{n}^n ≥ nx_{1} x_{2} · · · x_{n} $.

Showing the inequality $f(x)=x^{2(1-x)}+(1-x)^{2x}\leq 1$ for $0<x<1$

Random variable in $L^p$ implies random variable in $L^1$

Finding bounds for the absolute value of function raised to positive constant

Undertanding Jensen's inequality proof on countable basis Hilbert with Radon measure

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