List questions from cauchy-schwarz-inequality

Published on 16 Oct 2018 - 18:52

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How big does $r$ need to be, to ensure that $x^4+y^4 >r^2$ for all $x^2+y^2 =r^2$?

Published on 17 Oct 2018 - 4:10

58

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$\lVert tx +y\rVert\ge 0$, for all $t\in\mathbb R$, implies that $\,|\langle x,y\rangle|\le \lVert x\rVert \lVert y \rVert$

Published on 17 Oct 2018 - 22:08

44

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How to bound $(\frac{a}{x}+\frac{b}{y})(x+y)$ for large $x,y$ and positive $a,b$

Published on 18 Oct 2018 - 12:27

519

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prove $\frac{x}{(ay + bz)} + \frac{y}{(az + bx)} + \frac{z}{(ax + by)} ≥ \frac{3}{(a+b)}$

Published on 26 Mar 2026 - 17:33

51

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Need a hint on how to solve this inequality

Published on 20 Oct 2018 - 22:04

58

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Prove using squared number property

Published on 25 Mar 2026 - 9:44

100

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If $f$ is continuous and $3\geq f(x)\geq 1$ for all $x\in[0,1]$, show the integral inequality.

Published on 25 Mar 2026 - 12:29

78

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Inequality involving a kind of Harmonic mean

Published on 26 Mar 2026 - 9:49

87

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Finding maximum value of squared sum

Published on 04 Nov 2018 - 8:22

1.9k

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Kantorovich inequality and Cauchy-Schwarz inequality

Published on 05 Nov 2018 - 13:23

177

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What kind of "geometric" regularity $f'^2$ gives on $f$

Published on 26 Mar 2026 - 14:32

77

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Maximum length perimeter of a box whose diagonal is 10 unit long.

Published on 13 Nov 2018 - 19:41

120

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Remark 16 in Chapter 2 from Brezis - Functional Analysis, Sobolev Spaces, and Partial Differential Equations.

Published on 25 Mar 2026 - 6:02

125

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Proving $q:\mathbb{R}^n \to \mathbb{R} \text{ with } q(x):= x^TAx$ totally differentiable

Published on 15 Nov 2018 - 20:17

List Question

Prove Cauchy-Schwarz inequality

How big does $r$ need to be, to ensure that $x^4+y^4 >r^2$ for all $x^2+y^2 =r^2$?

$\lVert tx +y\rVert\ge 0$, for all $t\in\mathbb R$, implies that $\,|\langle x,y\rangle|\le \lVert x\rVert \lVert y \rVert$

How to bound $(\frac{a}{x}+\frac{b}{y})(x+y)$ for large $x,y$ and positive $a,b$

prove $\frac{x}{(ay + bz)} + \frac{y}{(az + bx)} + \frac{z}{(ax + by)} ≥ \frac{3}{(a+b)}$

Need a hint on how to solve this inequality

Prove using squared number property

If $f$ is continuous and $3\geq f(x)\geq 1$ for all $x\in[0,1]$, show the integral inequality.

Inequality involving a kind of Harmonic mean

Finding maximum value of squared sum

Kantorovich inequality and Cauchy-Schwarz inequality

What kind of "geometric" regularity $f'^2$ gives on $f$

Maximum length perimeter of a box whose diagonal is 10 unit long.

Remark 16 in Chapter 2 from Brezis - Functional Analysis, Sobolev Spaces, and Partial Differential Equations.

Proving $q:\mathbb{R}^n \to \mathbb{R} \text{ with } q(x):= x^TAx$ totally differentiable

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