List questions from convexity-inequality

Published on 25 Mar 2026 - 17:38

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Condition for convexity/strict convexity

Published on 25 Mar 2026 - 15:58

35

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inequality with sum and product

Published on 11 Apr 2026 - 8:27

118

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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 25 Mar 2026 - 17:40

116

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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 09 Apr 2026 - 12:13

55

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Convex order stochastic dominance for nonnegative integer valued random variables

Published on 24 Feb 2026 - 14:41

42

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

Published on 25 Mar 2026 - 15:58

24

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Proving that a given set defined by an inequality is convex

Published on 25 Mar 2026 - 16:00

54

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Convergence of blackbox sequence

Published on 25 Mar 2026 - 15:58

144

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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 25 Mar 2026 - 17:42

42

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Convex and Preinvex functions

Published on 25 Mar 2026 - 17:31

42

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

Published on 25 Mar 2026 - 19:10

229

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

Published on 25 Mar 2026 - 16:01

28

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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 25 Mar 2026 - 19:03

62

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

Published on 25 Mar 2026 - 16:03

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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