List questions from convexity-inequality

Published on 21 Feb 2021 - 17:18

429

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Concavity/ Convexity of power means function?

Published on 03 Apr 2021 - 18:26

114

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$\dfrac{e^t + e^{-t}}{2} \leq e^{ \frac{t^2}{2} } $

Published on 17 Apr 2021 - 16:36

915

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Prove or disprove that the function $f(x)=x^{x^{x^{x}}}$ is convex on $(0,1)$

Published on 08 Jun 2021 - 12:53

167

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Prove that: $\frac{1}{1+x+x^2+x^3}+\frac{1}{1+y+y^2+y^3}+\frac{1}{1+z+z^2+z^3}+\frac{1}{1+t+t^2+t^3}\ge1$

Published on 26 Jul 2021 - 15:09

92

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Prove or disprove that the function is convex on a certain interval

Published on 18 Aug 2021 - 13:38

80

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how to obtain the strong convexity inequality

Published on 13 Sep 2021 - 22:25

187

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Prove continuous $f$ is convex if and only if $\frac{f(x_2) - f(x_1)}{x_2 - x_1} \leq \frac{f(x_3) - f(x_1)}{x_3 - x_1}$ for $x_1 < x_2 < x_3$

Published on 25 Sep 2021 - 11:11

378

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Proof that $x^\frac{1}{p}$ is concave without derivative $(p>1)$

Published on 26 Sep 2021 - 11:11

63

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Convexity, concavity doubts

Published on 03 Oct 2021 - 11:20

19

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Convexity of a function defined on $W^{1,p}(]0,r[)$

Published on 16 Oct 2021 - 19:07

358

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strict convexity attains minimum

Published on 22 Dec 2021 - 1:30

44

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proof that sin (a + b + c)/3 ≥ 1/3 (sin a + sin b + sin c)

Published on 04 Jan 2022 - 19:15

341

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Convex function inequality with eigenvalues of Hessian matrix are bounded above and away from zero

Published on 14 Jan 2022 - 16:31

156

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Why is the negative $l^p$ norm like function convex when $0 < p < 1$?

Published on 23 Mar 2022 - 3:58

List Question

Strongly convex functions (equivalence and intuition)

Concavity/ Convexity of power means function?

$\dfrac{e^t + e^{-t}}{2} \leq e^{ \frac{t^2}{2} } $

Prove or disprove that the function $f(x)=x^{x^{x^{x}}}$ is convex on $(0,1)$

Prove that: $\frac{1}{1+x+x^2+x^3}+\frac{1}{1+y+y^2+y^3}+\frac{1}{1+z+z^2+z^3}+\frac{1}{1+t+t^2+t^3}\ge1$

Prove or disprove that the function is convex on a certain interval

how to obtain the strong convexity inequality

Prove continuous $f$ is convex if and only if $\frac{f(x_2) - f(x_1)}{x_2 - x_1} \leq \frac{f(x_3) - f(x_1)}{x_3 - x_1}$ for $x_1 < x_2 < x_3$

Proof that $x^\frac{1}{p}$ is concave without derivative $(p>1)$

Convexity, concavity doubts

Convexity of a function defined on $W^{1,p}(]0,r[)$

strict convexity attains minimum

proof that sin (a + b + c)/3 ≥ 1/3 (sin a + sin b + sin c)

Convex function inequality with eigenvalues of Hessian matrix are bounded above and away from zero

Why is the negative $l^p$ norm like function convex when $0 < p < 1$?

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