List questions from convexity-inequality

Published on 06 Sep 2019 - 13:12

199

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If $0\le a,b,c\le 1$, then $\frac a{1+bc}+\frac b{1+ac}+\frac c{1+ab}\le 2$

Published on 31 Dec 2014 - 12:04

1.2k

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Show that the ellipsoid is convex

Published on 03 Oct 2019 - 7:54

40

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Inequality with variable expoent

Published on 25 Mar 2026 - 6:13

34

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Jensen midpoint inequality reference lost

Published on 15 Nov 2019 - 14:18

413

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A bilinear matrix inequality

Published on 23 Nov 2019 - 17:47

285

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Characterization of convexity with a gradient formula almost everywhere

Published on 26 Feb 2026 - 12:36

66

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Prove an inequality : $\sum_{cyc}\frac{a^3}{abu+b^2v}\geq \frac{a+b+c}{u+v}$ without Jensen's inequality

Published on 23 Mar 2026 - 0:40

28

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Strict Convex function

Published on 03 Dec 2019 - 8:44

77

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Show $\prod_{i=1}^n (1 - t + t a_i) \geq 1$ when $\prod_{i=1}^n a_i = 1$

Published on 04 Dec 2019 - 18:34

213

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An inequality without studying variations

Published on 04 Jan 2020 - 22:45

47

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show that $| f+g | ^p \leq s^{1-p}| f| ^p + (1-s)^{1-p}| g| ^p$

Published on 16 Jan 2020 - 9:45

305

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An exponential equation over positive real numbers $4^x+14^x+3^x=11^x+10^x$

Published on 05 Feb 2020 - 11:17

229

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A special case of Karamata's inequality to solve one or more Olympiad inequality?

Published on 24 Mar 2026 - 14:55

55

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How to prove $a\ln(1+x_1)+(1-a)\ln(1+x_2)\le \ln(1+x)$ for $a\in(0,1)$ and $x_1+x_2=x$

Published on 02 Mar 2020 - 4:13

List Question

Simil convexity inequality

If $0\le a,b,c\le 1$, then $\frac a{1+bc}+\frac b{1+ac}+\frac c{1+ab}\le 2$

Show that the ellipsoid is convex

Inequality with variable expoent

Jensen midpoint inequality reference lost

A bilinear matrix inequality

Characterization of convexity with a gradient formula almost everywhere

Prove an inequality : $\sum_{cyc}\frac{a^3}{abu+b^2v}\geq \frac{a+b+c}{u+v}$ without Jensen's inequality

Strict Convex function

Show $\prod_{i=1}^n (1 - t + t a_i) \geq 1$ when $\prod_{i=1}^n a_i = 1$

An inequality without studying variations

show that $| f+g | ^p \leq s^{1-p}| f| ^p + (1-s)^{1-p}| g| ^p$

An exponential equation over positive real numbers $4^x+14^x+3^x=11^x+10^x$

A special case of Karamata's inequality to solve one or more Olympiad inequality?

How to prove $a\ln(1+x_1)+(1-a)\ln(1+x_2)\le \ln(1+x)$ for $a\in(0,1)$ and $x_1+x_2=x$

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