List questions from cauchy-schwarz-inequality

Published on 26 Mar 2026 - 8:23

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Interpreting an olympiad inequality as a convex function

Published on 28 Mar 2026 - 3:25

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How Can I Solve This Inequality Using Environmental Inequality?

Published on 28 Mar 2026 - 3:26

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Cauchy-Schwarz inequality in $L^2$

Published on 17 Mar 2020 - 3:56

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if $\sum_{k=1}^\infty \|x_k\|$ converges , then $\sum_{k=1}^\infty x_k$ also converges.

Published on 17 Mar 2020 - 4:18

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If $a^2+b^2+c^2 =3$, find the minimum value of $a+b+c$

Published on 29 Mar 2026 - 10:16

102

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Prove that $a b \leq \frac{a^{3}}{3}+\frac{b^{3 / 2}}{3 / 2}$

Published on 25 Mar 2026 - 6:12

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Bound the equation

Published on 27 Mar 2026 - 16:09

324

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Prove that $\sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ac+b} \ge 1+\sqrt{ab}+\sqrt{bc}+\sqrt{ac}$

Published on 25 Mar 2026 - 12:41

221

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Inequality for Olympiad students

Published on 25 Mar 2026 - 14:19

126

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If $abcd=1$ prove that $\frac{1+ab}{1+a}+\frac{1+bc}{1+b}+\frac{1+cd}{1+c}+\frac{1+ad}{1+d} \ge 4$

Published on 28 Mar 2026 - 3:27

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extension of cauchy schwarz inequality

Published on 22 Mar 2020 - 12:32

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Cauchy-Schwarz inequality for $a_1^4 + a_2^4 + \cdots + a_n^4 \geqslant n$

Published on 25 Mar 2026 - 4:41

162

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Is it possible to prove the triangle inequality in inner product spaces without using the Cauchy-Schwartz inequality?

Published on 23 Feb 2026 - 1:07

162

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$ Ax\cdot x>0$ and $Ay\cdot y>0$ implies $(Ax\cdot x)(Ay\cdot y)\geq (Ax\cdot y)^2$?

Published on 28 Mar 2026 - 14:44

List Question

A geometric inequality for acute triangle $\sum \sqrt \frac{b^2+c^2-a^2}{a^2+2bc} \leq \sqrt3$

Interpreting an olympiad inequality as a convex function

How Can I Solve This Inequality Using Environmental Inequality?

Cauchy-Schwarz inequality in $L^2$

if $\sum_{k=1}^\infty \|x_k\|$ converges , then $\sum_{k=1}^\infty x_k$ also converges.

If $a^2+b^2+c^2 =3$, find the minimum value of $a+b+c$

Prove that $a b \leq \frac{a^{3}}{3}+\frac{b^{3 / 2}}{3 / 2}$

Bound the equation

Prove that $\sqrt{ab+c}+\sqrt{bc+a}+\sqrt{ac+b} \ge 1+\sqrt{ab}+\sqrt{bc}+\sqrt{ac}$

Inequality for Olympiad students

If $abcd=1$ prove that $\frac{1+ab}{1+a}+\frac{1+bc}{1+b}+\frac{1+cd}{1+c}+\frac{1+ad}{1+d} \ge 4$

extension of cauchy schwarz inequality

Cauchy-Schwarz inequality for $a_1^4 + a_2^4 + \cdots + a_n^4 \geqslant n$

Is it possible to prove the triangle inequality in inner product spaces without using the Cauchy-Schwartz inequality?

$ Ax\cdot x>0$ and $Ay\cdot y>0$ implies $(Ax\cdot x)(Ay\cdot y)\geq (Ax\cdot y)^2$?

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