List questions from jensen-inequality

Published on 26 Nov 2018 - 19:04

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Jensen's type inequality for inner product

Published on 29 Nov 2018 - 22:01

378

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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

150

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Proof verification: For $a$, $b$, $c$ positive with $abc=1$, show $\sum_{\text{cyc}}\frac{1}{a^3(b+c)}\geq \frac32$

Published on 16 Dec 2018 - 19:49

140

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An inequality for convex function from $\mathbb R$ to $\mathbb R$

Published on 19 Dec 2018 - 14:13

87

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How can we show that $\left|a+b+c\right|^p-2\left|a\right|^p\le C\left(\left|b\right|^p+\left|c\right|^p\right)$?

Published on 22 Dec 2018 - 13:16

112

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Can Jensen be applied to multivariable functions?

Published on 23 Dec 2018 - 13:41

262

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How can I prove that $\frac{e^x+e^y}{2}>e^\frac{x+y}{2}$, where $x \neq y$?

Published on 24 Dec 2018 - 18:25

1.7k

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Kovari-Sos-Turan Theorem - proof

Published on 09 Jan 2019 - 19:23

157

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A conjecture about power sum : $e^{ab}+e^{bc}+e^{ca}\geq 3e^{\sqrt{abc}}$ and $a+b+c=3$

Published on 01 Feb 2019 - 13:21

184

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Generalization of Nesbitts's inequality

Published on 22 Mar 2026 - 8:35

1k

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Find maximum of $\cos(x)\cos(y)\cos(z)$ when $x + y + z = \frac{\pi}{2}$ and $x, y, z > 0$

Published on 02 Feb 2019 - 5:49

124

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Proving a (seemingly simple) inequality

Published on 08 Feb 2019 - 8:51

71

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Prove that $ (\frac{\sum_{i=1}^n x_i}{n})^{\sum_{i=1}^n x_i} \le \prod_{i=1}^n {x_i}^{x_i}$ $, \forall x_i>0, n\ge1 $

Published on 09 Feb 2019 - 14:40

190

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Proving inequality using Jensen

Published on 14 Feb 2019 - 17:26

List Question

Upperbounding the expected value of an L2-norm difference

Jensen's type inequality for inner product

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

Proof verification: For $a$, $b$, $c$ positive with $abc=1$, show $\sum_{\text{cyc}}\frac{1}{a^3(b+c)}\geq \frac32$

An inequality for convex function from $\mathbb R$ to $\mathbb R$

How can we show that $\left|a+b+c\right|^p-2\left|a\right|^p\le C\left(\left|b\right|^p+\left|c\right|^p\right)$?

Can Jensen be applied to multivariable functions?

How can I prove that $\frac{e^x+e^y}{2}>e^\frac{x+y}{2}$, where $x \neq y$?

Kovari-Sos-Turan Theorem - proof

A conjecture about power sum : $e^{ab}+e^{bc}+e^{ca}\geq 3e^{\sqrt{abc}}$ and $a+b+c=3$

Generalization of Nesbitts's inequality

Find maximum of $\cos(x)\cos(y)\cos(z)$ when $x + y + z = \frac{\pi}{2}$ and $x, y, z > 0$

Proving a (seemingly simple) inequality

Prove that $ (\frac{\sum_{i=1}^n x_i}{n})^{\sum_{i=1}^n x_i} \le \prod_{i=1}^n {x_i}^{x_i}$ $, \forall x_i>0, n\ge1 $

Proving inequality using Jensen

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