List questions from convexity-inequality

Published on 25 Mar 2026 - 22:10

430

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Concavity/ Convexity of power means function?

Published on 25 Mar 2026 - 22:10

115

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

Published on 26 Mar 2026 - 1:02

916

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

Published on 25 Mar 2026 - 22:04

168

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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 Mar 2026 - 1:12

93

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

Published on 26 Mar 2026 - 1:02

81

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how to obtain the strong convexity inequality

Published on 25 Mar 2026 - 22:03

188

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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 26 Mar 2026 - 1:12

379

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

Published on 25 Mar 2026 - 22:03

64

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Convexity, concavity doubts

Published on 26 Mar 2026 - 1:27

20

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

Published on 25 Mar 2026 - 23:36

359

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strict convexity attains minimum

Published on 25 Mar 2026 - 23:35

45

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

Published on 25 Mar 2026 - 22:10

342

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

Published on 26 Mar 2026 - 1:03

157

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

Published on 25 Mar 2026 - 22:10

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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