List questions from convexity-inequality

Published on 10 Apr 2026 - 17:47

200

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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 25 Mar 2026 - 8:10

1.2k

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Show that the ellipsoid is convex

Published on 09 Apr 2026 - 11:18

43

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Inequality with variable expoent

Published on 10 May 2026 - 14:28

35

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Jensen midpoint inequality reference lost

Published on 25 Mar 2026 - 8:11

418

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A bilinear matrix inequality

Published on 05 May 2026 - 21:03

286

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Characterization of convexity with a gradient formula almost everywhere

Published on 11 Apr 2026 - 21:39

69

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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 17 Apr 2026 - 23:11

32

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Strict Convex function

Published on 24 Apr 2026 - 6:47

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

215

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An inequality without studying variations

Published on 27 Mar 2026 - 10:25

48

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

Published on 25 Mar 2026 - 8:13

306

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

Published on 25 Mar 2026 - 8:12

232

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

Published on 10 May 2026 - 16:35

56

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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 25 Mar 2026 - 8:13

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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