List questions from convexity-inequality

Published on 12 Jul 2023 - 7:31

19

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Condition for convexity/strict convexity

Published on 18 Jul 2023 - 17:23

31

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inequality with sum and product

Published on 30 Jul 2023 - 13:07

117

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If $a,b,c >0 : ab+bc+ca=3,$ find maximal value $\sum\dfrac{a\sqrt{a^2+2}}{a^2+3}$

Published on 04 Aug 2023 - 4:20

115

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For $x+y+z=3,$ prove $\frac{1}{x^2+4}+\frac{1}{y^2+4}+\frac{1}{z^2+4}\le \frac{3}{5}.$

Published on 23 Feb 2026 - 8:05

55

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Convex order stochastic dominance for nonnegative integer valued random variables

Published on 24 Feb 2026 - 14:41

41

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Proof a set is affine, a cone, a convex set

Published on 05 Oct 2023 - 11:24

23

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Proving that a given set defined by an inequality is convex

Published on 12 Oct 2023 - 19:08

53

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Convergence of blackbox sequence

Published on 22 Oct 2023 - 21:27

143

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Prove $\sqrt{\frac{a+4bc}{4a+bc}}+\sqrt{\frac{b+4ca}{4b+ac}}+\sqrt{\frac{c+4ab}{4c+ab}}\ge 3,$ when $a+b+c=3.$

Published on 28 Oct 2023 - 9:25

41

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Convex and Preinvex functions

Published on 28 Oct 2023 - 16:09

41

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Confused of one step of proofing convexity of a function related to LP

Published on 07 Nov 2023 - 3:16

228

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Log-convexity of a function defined by an integral (Normal Mills ratio)

Published on 26 Dec 2023 - 9:26

27

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Showing that a function $\varphi$ is convex if $\varphi\left(\int_{0}^{1}f(x) d\lambda(x)\right) \leq \int_{0}^{1}\varphi(f(x))d\lambda(x)$

Published on 23 Jan 2024 - 11:09

61

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Proving the Preposition: Log-Convexity of a Function and the Monotonicity of Ratios

Published on 16 Feb 2024 - 6:22

List Question

What is a convex set $S = \mathbb{R}_{++}^2$

Condition for convexity/strict convexity

inequality with sum and product

If $a,b,c >0 : ab+bc+ca=3,$ find maximal value $\sum\dfrac{a\sqrt{a^2+2}}{a^2+3}$

For $x+y+z=3,$ prove $\frac{1}{x^2+4}+\frac{1}{y^2+4}+\frac{1}{z^2+4}\le \frac{3}{5}.$

Convex order stochastic dominance for nonnegative integer valued random variables

Proof a set is affine, a cone, a convex set

Proving that a given set defined by an inequality is convex

Convergence of blackbox sequence

Prove $\sqrt{\frac{a+4bc}{4a+bc}}+\sqrt{\frac{b+4ca}{4b+ac}}+\sqrt{\frac{c+4ab}{4c+ab}}\ge 3,$ when $a+b+c=3.$

Convex and Preinvex functions

Confused of one step of proofing convexity of a function related to LP

Log-convexity of a function defined by an integral (Normal Mills ratio)

Showing that a function $\varphi$ is convex if $\varphi\left(\int_{0}^{1}f(x) d\lambda(x)\right) \leq \int_{0}^{1}\varphi(f(x))d\lambda(x)$

Proving the Preposition: Log-Convexity of a Function and the Monotonicity of Ratios

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