List questions from jensen-inequality

Published on 05 Jan 2014 - 19:36

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Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$

Published on 25 Mar 2026 - 7:45

157

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Prove this $(ab)^2+(bc)^2+(ca)^2\le ab+bc+ac$

Published on 14 Apr 2017 - 13:23

206

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Maximum area of pentagon in the quarter circle

Published on 22 Apr 2017 - 22:02

246

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$a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$

Published on 25 Mar 2026 - 12:27

221

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Minimum value of $\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$

Published on 19 May 2017 - 10:41

1.2k

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Inequality in real analysis $x^a y^{1-a} \le ax+ (1-a)y$

Published on 21 May 2017 - 13:36

89

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Petrovic and Jensen inequaltiy

Published on 25 Mar 2026 - 6:27

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If $b>a,$ find the minimum value of $|(x-a)^3|+|(x-b)^3|,x\in R$

Published on 17 Jun 2017 - 16:10

122

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Minimize $x^4+ \frac{1}{x^4} +y^4+ \frac{1}{y^4}$

Published on 31 Jul 2017 - 12:28

144

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How prove this in equality with $abc=1$

Published on 02 Aug 2017 - 15:49

75

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Need help with the following inequality

Published on 03 Aug 2017 - 5:27

194

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Upper bound on $\mathbb{E}[X^2]$

Published on 08 Aug 2017 - 1:47

157

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A nice inequality with positive real tuples

Published on 09 Aug 2017 - 21:02

209

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rudin real analysis chapter3 Q3

Published on 12 Aug 2017 - 6:43

List Question

When Jensen's inequality is equality

Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$

Prove this $(ab)^2+(bc)^2+(ca)^2\le ab+bc+ac$

Maximum area of pentagon in the quarter circle

$a+b+c = 3$, prove that :$a\sqrt{a+3}+b\sqrt{b+3}+c\sqrt{c+3} \geq 6$

Minimum value of $\left(a+\frac{1}{b}\right)^2+\left(b+\frac{1}{c}\right)^2+\left(c+\frac{1}{a}\right)^2$

Inequality in real analysis $x^a y^{1-a} \le ax+ (1-a)y$

Petrovic and Jensen inequaltiy

If $b>a,$ find the minimum value of $|(x-a)^3|+|(x-b)^3|,x\in R$

Minimize $x^4+ \frac{1}{x^4} +y^4+ \frac{1}{y^4}$

How prove this in equality with $abc=1$

Need help with the following inequality

Upper bound on $\mathbb{E}[X^2]$

A nice inequality with positive real tuples

rudin real analysis chapter3 Q3

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