Question

If $f(\frac{t_1+t_2}{2}) \leq \frac{f(t_1)+f(t_2)}{2}$, show that $f(\frac{t_1+t_2+ \cdots +t_n}{n})\leq \frac{f(t_1)+f(t_2)+\cdots f(t_n)}{n}$

score 181 · Answer 1 · 2020-04-30 09:58:02

181

Views

If $f(\frac{t_1+t_2}{2}) \leq \frac{f(t_1)+f(t_2)}{2}$, show that $f(\frac{t_1+t_2+ \cdots +t_n}{n})\leq \frac{f(t_1)+f(t_2)+\cdots f(t_n)}{n}$

Published on 30 Apr 2020 - 9:58

score 306 · Answer 2 · 2026-03-25 12:47:19

306

Views

MOP 2011 inequality

Published on 25 Mar 2026 - 12:47

score 225 · Answer 3 · 2026-03-16 13:24:56

225

Views

Prove using Jensen's inequality that if $abcd=1$ then $\frac{1}{(1+a)^{2}}+\frac{1}{(1+b)^{2}}+\frac{1}{(1+c)^{2}}+\frac{1}{(1+d)^{2}} \geq 1$

Published on 16 Mar 2026 - 13:24

score 308 · Answer 4 · 2020-05-03 12:01:05

308

Views

What is the proof of entropy property: $H\left(x,y\right)\le H\left(x\right)+H\left(y\right)$ in Shannon's paper?

Published on 03 May 2020 - 12:01

score 133 · Answer 5 · 2020-05-05 12:43:52

133

Views

If $x+y+z=1$ prove $ \sqrt{x+\frac{(y-z)^{2}}{12}}+\sqrt{y+\frac{(z-x)^{2}}{12}}+\sqrt{z+\frac{(x-y)^{2}}{12}} \leq \sqrt{3} $

Published on 05 May 2020 - 12:43

score 264 · Answer 6 · 2020-05-09 11:40:28

264

Views

Can I apply Jensen Inequality here?

Published on 09 May 2020 - 11:40

score 623 · Answer 7 · 2020-05-13 12:45:36

623

Views

Exercise on submartingales: is $\phi(X_n)$ a submartingale, given some assumptions on $(X_n)$? Is the following solution correct?

Published on 13 May 2020 - 12:45

score 164 · Answer 8 · 2020-05-14 03:24:24

$a+b+c+d=1, a,b,c,d ≠ 0$, then prove that $(a + \frac{1}{a})^2 + (b + \frac{1}{b})^2 + (c + \frac{1}{c})^2 + (d + \frac{1}{d})^2 \ge \frac{289}{4} $

score 178 · Answer 9 · 2026-03-25 07:47:32

178

Views

Question regarding Jensen Inequality

Published on 25 Mar 2026 - 7:47

score 257 · Answer 10 · 2020-05-16 18:00:51

257

Views

Conjecture about Jensen's inequality and polynomials

Published on 16 May 2020 - 18:00

score 92 · Answer 11 · 2020-05-19 06:49:41

92

Views

References for variants of Jensen inequality

Published on 19 May 2020 - 6:49

score 562 · Answer 12 · 2020-05-24 22:36:06

562

Views

Some doubts in a part of the proof of Backwards Martingale Convergence Theorem (Jacod-Protter)

Published on 24 May 2020 - 22:36

score 162 · Answer 13 · 2020-05-31 11:28:56

162

Views

sum of exponential vs exponential of sums

Published on 31 May 2020 - 11:28

score 96 · Answer 14 · 2020-06-01 12:34:09

96

Views

$f(0)=f(1)=0$, $f(x)=\frac{f(x+h)+f(x-h)}{2}$ implies $f(x)=0$ for $[0, 1]$

Published on 01 Jun 2020 - 12:34

score 296 · Answer 15 · 2020-06-03 00:45:52

296

Views

Use Jensen's inequality to show $\frac{2x}{2+x} < \log(1+x) < \frac{2x+x^2}{2+2x}$ for $x>0$

Published on 03 Jun 2020 - 0:45

List Question

If $f(\frac{t_1+t_2}{2}) \leq \frac{f(t_1)+f(t_2)}{2}$, show that $f(\frac{t_1+t_2+ \cdots +t_n}{n})\leq \frac{f(t_1)+f(t_2)+\cdots f(t_n)}{n}$

MOP 2011 inequality

Prove using Jensen's inequality that if $abcd=1$ then $\frac{1}{(1+a)^{2}}+\frac{1}{(1+b)^{2}}+\frac{1}{(1+c)^{2}}+\frac{1}{(1+d)^{2}} \geq 1$

What is the proof of entropy property: $H\left(x,y\right)\le H\left(x\right)+H\left(y\right)$ in Shannon's paper?

If $x+y+z=1$ prove $ \sqrt{x+\frac{(y-z)^{2}}{12}}+\sqrt{y+\frac{(z-x)^{2}}{12}}+\sqrt{z+\frac{(x-y)^{2}}{12}} \leq \sqrt{3} $

Can I apply Jensen Inequality here?

Exercise on submartingales: is $\phi(X_n)$ a submartingale, given some assumptions on $(X_n)$? Is the following solution correct?

$a+b+c+d=1, a,b,c,d ≠ 0$, then prove that $(a + \frac{1}{a})^2 + (b + \frac{1}{b})^2 + (c + \frac{1}{c})^2 + (d + \frac{1}{d})^2 \ge \frac{289}{4} $

Question regarding Jensen Inequality

Conjecture about Jensen's inequality and polynomials

References for variants of Jensen inequality

Some doubts in a part of the proof of Backwards Martingale Convergence Theorem (Jacod-Protter)

sum of exponential vs exponential of sums

$f(0)=f(1)=0$, $f(x)=\frac{f(x+h)+f(x-h)}{2}$ implies $f(x)=0$ for $[0, 1]$

Use Jensen's inequality to show $\frac{2x}{2+x} < \log(1+x) < \frac{2x+x^2}{2+2x}$ for $x>0$

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