List questions from jensen-inequality

Published on 31 Aug 2023 - 22:34

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Is this Jensen's Inequality? (Symmetrization Lemma)

Published on 14 Sep 2023 - 20:25

62

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Does the Jensen's inequality hold under expectation?

Published on 19 Sep 2023 - 20:58

83

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The inequality of convex function including power function

Published on 21 Sep 2023 - 15:57

32

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Ratio of two Jensen's Inequality

Published on 22 Sep 2023 - 1:38

27

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Relationship between the expectation of the squared L2 norm of sum of elements and the sum of expectations of squared L2 norm of elements.

Published on 25 Sep 2023 - 17:17

478

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$X$ is sub-Gaussian, then $X^2$ is sub-exponential

Published on 30 Sep 2023 - 5:32

37

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Entrywise matrix Jensen inequality?

Published on 08 Oct 2023 - 2:02

25

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Bounding sum with weights changed from $2^{a_i}$ to $a_i$

Published on 12 Oct 2023 - 13:13

108

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How to prove this inequality $\sum_{r=1}^{n}a_{r}\sqrt{\frac{n-1}{1-a_{r}}}\ge\sum_{r=1}^{n}\sqrt{a_{r}}$

Published on 14 Oct 2023 - 10:31

173

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How to prove $\sqrt{4a+1}+\sqrt{4b+1}+\sqrt{4c+1}\ge \frac{\sqrt{abc+4}+4\sqrt{ab+bc+ca+4}}{2}.$

Published on 07 Nov 2023 - 13:56

39

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Jensen's inequality for composite functions

Published on 16 Nov 2023 - 13:34

68

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Does $E^2(X)/E(Y) \le E(X^2/Y)$ hold

Published on 21 Nov 2023 - 12:19

90

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Prove $\frac{1}{\sqrt{2a+b+c}}+\frac{1}{\sqrt{2b+a+c}}+\frac{1}{\sqrt{2c+b+a}}\le \frac{9}{2}\cdot\frac{1}{\sqrt{a}+\sqrt{b}+\sqrt{c}}.$

Published on 25 Nov 2023 - 3:37

140

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Finding $\small{\min\limits_{a+b+c=2}\sqrt{a-2bc+3}+\sqrt{b-2ca+3}+\sqrt{c-2ab+3}.}$

Published on 25 Mar 2026 - 14:38

List Question

Jensen's inequality integral version for strongly convex functions

Is this Jensen's Inequality? (Symmetrization Lemma)

Does the Jensen's inequality hold under expectation?

The inequality of convex function including power function

Ratio of two Jensen's Inequality

Relationship between the expectation of the squared L2 norm of sum of elements and the sum of expectations of squared L2 norm of elements.

$X$ is sub-Gaussian, then $X^2$ is sub-exponential

Entrywise matrix Jensen inequality?

Bounding sum with weights changed from $2^{a_i}$ to $a_i$

How to prove this inequality $\sum_{r=1}^{n}a_{r}\sqrt{\frac{n-1}{1-a_{r}}}\ge\sum_{r=1}^{n}\sqrt{a_{r}}$

How to prove $\sqrt{4a+1}+\sqrt{4b+1}+\sqrt{4c+1}\ge \frac{\sqrt{abc+4}+4\sqrt{ab+bc+ca+4}}{2}.$

Jensen's inequality for composite functions

Does $E^2(X)/E(Y) \le E(X^2/Y)$ hold

Prove $\frac{1}{\sqrt{2a+b+c}}+\frac{1}{\sqrt{2b+a+c}}+\frac{1}{\sqrt{2c+b+a}}\le \frac{9}{2}\cdot\frac{1}{\sqrt{a}+\sqrt{b}+\sqrt{c}}.$

Finding $\small{\min\limits_{a+b+c=2}\sqrt{a-2bc+3}+\sqrt{b-2ca+3}+\sqrt{c-2ab+3}.}$

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