List questions from holder-inequality

Published on 25 Mar 2026 - 16:13

110

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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

131

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prove that $\frac{2}{b(a+b)}+\frac{2}{c(b+c)}+\frac{2}{a(c+a)} \ge \frac{27}{(a+b+c)^2}$

Published on 25 Mar 2026 - 16:13

110

Views

Roots of the equation $(1-4x)^4+32x^4=\frac{1}{27}$

Published on 25 Mar 2026 - 16:13

109

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An inequality involving homogeneous polynomials

Published on 25 Mar 2026 - 16:13

226

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Reciprocal of Holder's inequality

Published on 25 Mar 2026 - 16:13

452

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Applying Hölder inequality to prove $\Vert x \Vert_p \leq n^{\frac{1}{p}-\frac{1}{q}} \Vert x \Vert_q$

Published on 25 Mar 2026 - 16:20

75

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Reciprocal of Hölder's inequality

Published on 25 Mar 2026 - 16:13

50

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Clarifying a step in the equality case of the Hölders inequalite

Published on 25 Mar 2026 - 16:13

187

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If $a+b+c+d=4$ Prove that $ \sqrt{\frac{a+1}{a b+1}}+\sqrt{\frac{b+1}{b c+1}}+\sqrt{\frac{c+1}{c d+1}}+\sqrt{\frac{d+1}{d a+1}} \geq 4 $

Published on 25 Mar 2026 - 16:20

279

Views

$\sum\limits_{cyc}\frac{a}{\sqrt{a+3b}}\geq\frac{a+b+c}{2}$ for $a+b+c+abc=4$

Published on 25 Mar 2026 - 16:14

113

Views

Olympiad Inequality: Cauchy Schwartz

Published on 25 Mar 2026 - 16:13

163

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prove that $3(a+b+c) \geq 8(a b c)^{1 / 3}+\left(\frac{a^{3}+b^{3}+c^{3}}{3}\right)^{1 / 3}$

Published on 11 May 2026 - 3:17

877

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Holder's Inequality for $0<p<1$

Published on 25 Mar 2026 - 17:52

82

Views

Using Holder and C-S to prove the radical inequality.

Published on 25 Mar 2026 - 16:21

List Question

For non-negative reals $a$, $b$, $c$, show that $3(1-a+a^2)(1-b+b^2)(1-c+c^2)\ge(1+abc+a^2b^2c^2)$

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

prove that $\frac{2}{b(a+b)}+\frac{2}{c(b+c)}+\frac{2}{a(c+a)} \ge \frac{27}{(a+b+c)^2}$

Roots of the equation $(1-4x)^4+32x^4=\frac{1}{27}$

An inequality involving homogeneous polynomials

Reciprocal of Holder's inequality

Applying Hölder inequality to prove $\Vert x \Vert_p \leq n^{\frac{1}{p}-\frac{1}{q}} \Vert x \Vert_q$

Reciprocal of Hölder's inequality

Clarifying a step in the equality case of the Hölders inequalite

If $a+b+c+d=4$ Prove that $ \sqrt{\frac{a+1}{a b+1}}+\sqrt{\frac{b+1}{b c+1}}+\sqrt{\frac{c+1}{c d+1}}+\sqrt{\frac{d+1}{d a+1}} \geq 4 $

$\sum\limits_{cyc}\frac{a}{\sqrt{a+3b}}\geq\frac{a+b+c}{2}$ for $a+b+c+abc=4$

Olympiad Inequality: Cauchy Schwartz

prove that $3(a+b+c) \geq 8(a b c)^{1 / 3}+\left(\frac{a^{3}+b^{3}+c^{3}}{3}\right)^{1 / 3}$

Holder's Inequality for $0<p<1$

Using Holder and C-S to prove the radical inequality.

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