List questions from jensen-inequality

Published on 30 Nov 2023 - 19:12

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Can anyone help prove or disprove that $\frac{\Pi_i x_i ^\frac{x_i}{1+\sum_i x_i}}{1+\sum_i x_i} \geq \frac{1}{N+1}$, where $x_i>0$

Published on 02 Dec 2023 - 22:33

17

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Upper bound on E[ln(X)^2]

Published on 22 Dec 2023 - 11:41

31

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Bound on Jensen's gap for bivariate functions

Published on 25 Mar 2026 - 15:47

93

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Prove an inequality using Jensen's inequality

Published on 18 Jan 2024 - 20:43

89

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Show $\left(x_1x_2\ldots x_n\right)^{\frac{x_1+\cdots +x_n}{n}}\le x_1^{x_1}x_2^{x_2}\ldots x_n^{x_n}$

Published on 08 Feb 2024 - 17:41

41

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Case of equality in Jensen's Inequality

Published on 22 Feb 2024 - 14:07

257

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Showing $\frac1{ab+4}+\frac1{ac+4}+\frac1{ad+4}+\frac1{bc+4}+\frac1{bd+4}+\frac1{cd+4}\geq\frac65$, for positive $a,b,c,d$ with $ab+bc+cd+da=4$

Published on 25 Mar 2026 - 18:57

68

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Elementary proof that $\mathbb{E}[1/X] \geq 1/\mathbb{E}[X]$ for finitely supported positive random variables.

Published on 06 Mar 2024 - 20:31

32

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Prove the following from Jensen's inequality

Published on 09 Mar 2024 - 17:33

243

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Showing inequality involving log

Published on 13 Mar 2024 - 19:07

58

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Show the inequality $\sum_{\text{cyc}} \sqrt{\frac{a^3}{b^3 + (c+a)^3}} \ge 1$

Published on 28 Mar 2024 - 12:42

40

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Integral Jensen Inequality

Published on 28 Mar 2024 - 21:33

4.1k

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Prove QM-AM inequality

Published on 24 Apr 2015 - 14:57

1.9k

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Jensen's inequality; what's the need for the probability measure?

Published on 05 Mar 2016 - 15:17

List Question

How to prove $x^{x/(1+x)}/(1+x)\geq1/2$

Can anyone help prove or disprove that $\frac{\Pi_i x_i ^\frac{x_i}{1+\sum_i x_i}}{1+\sum_i x_i} \geq \frac{1}{N+1}$, where $x_i>0$

Upper bound on E[ln(X)^2]

Bound on Jensen's gap for bivariate functions

Prove an inequality using Jensen's inequality

Show $\left(x_1x_2\ldots x_n\right)^{\frac{x_1+\cdots +x_n}{n}}\le x_1^{x_1}x_2^{x_2}\ldots x_n^{x_n}$

Case of equality in Jensen's Inequality

Showing $\frac1{ab+4}+\frac1{ac+4}+\frac1{ad+4}+\frac1{bc+4}+\frac1{bd+4}+\frac1{cd+4}\geq\frac65$, for positive $a,b,c,d$ with $ab+bc+cd+da=4$

Elementary proof that $\mathbb{E}[1/X] \geq 1/\mathbb{E}[X]$ for finitely supported positive random variables.

Prove the following from Jensen's inequality

Showing inequality involving log

Show the inequality $\sum_{\text{cyc}} \sqrt{\frac{a^3}{b^3 + (c+a)^3}} \ge 1$

Integral Jensen Inequality

Prove QM-AM inequality

Jensen's inequality; what's the need for the probability measure?

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