List questions from holder-inequality

Published on 25 Mar 2026 - 10:56

187

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Given positives $a, b, c$, prove that $\frac{a}{(b + c)^2} + \frac{b}{(c + a)^2} + \frac{c}{(a + b)^2} \ge \frac{9}{4(a + b + c)}$.

Published on 10 May 2026 - 16:35

107

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Knowing that $\prod_{i = 1}^na_i = 1$, prove that $\prod_{i = 1}^n(a_i + 1)^{i + 1} > (n + 1)^{n + 1}$.

Published on 25 Mar 2026 - 14:36

204

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Cyclic Inequality $(x^8+1)(x^4+1)(y^8+1)(y^4+1)(z^8+1)(z^4+1)≥((x^2+1)(y^2+1)(z^2+1))^2$

Published on 25 Mar 2026 - 14:35

49

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Norm of adjoint via Hölder conjugates

Published on 25 Mar 2026 - 14:37

49

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Solving an Inequality problem

Published on 25 Mar 2026 - 14:28

160

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Hölder' inequality for random variables

Published on 25 Mar 2026 - 14:28

31

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How to prove $\sum_{i=1}^{k}x_i^2\ge k$ if $\sum_{i=1}^{k}\frac{1}{x_i}=k$ and $\min (x_i-1)^2$ is sufficiently small?

Published on 10 May 2026 - 16:35

173

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Type of Holder Inequality

Published on 25 Mar 2026 - 14:32

457

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Barnard and Child inequality exercise

Published on 10 May 2026 - 21:47

88

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Holder inequality Proof Explanation

Published on 25 Mar 2026 - 14:28

33

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Estimates with $L^n$ norm

Published on 25 Mar 2026 - 14:32

127

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Prove $\sqrt[3]{\frac{(a^4+b^4)(a^4+c^4)(b^4+c^4)}{abc}}\ge \sqrt{\frac{(a^3+bc)(b^3+ca)(c^3+ab)}{1+abc}}$

Published on 25 Mar 2026 - 14:36

578

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Find an upper bound on the expectation of squared norm given an upper bound on the expectation of norm

Published on 25 Mar 2026 - 14:36

93

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Inequality with condition $2(x^2+y^2+z^2)\leq 3(x+y+z-1)$

Published on 25 Mar 2026 - 14:34

List Question

Holder semi norm estimate for a solution of Poisson's equation in the half space

Given positives $a, b, c$, prove that $\frac{a}{(b + c)^2} + \frac{b}{(c + a)^2} + \frac{c}{(a + b)^2} \ge \frac{9}{4(a + b + c)}$.

Knowing that $\prod_{i = 1}^na_i = 1$, prove that $\prod_{i = 1}^n(a_i + 1)^{i + 1} > (n + 1)^{n + 1}$.

Cyclic Inequality $(x^8+1)(x^4+1)(y^8+1)(y^4+1)(z^8+1)(z^4+1)≥((x^2+1)(y^2+1)(z^2+1))^2$

Norm of adjoint via Hölder conjugates

Solving an Inequality problem

Hölder' inequality for random variables

How to prove $\sum_{i=1}^{k}x_i^2\ge k$ if $\sum_{i=1}^{k}\frac{1}{x_i}=k$ and $\min (x_i-1)^2$ is sufficiently small?

Type of Holder Inequality

Barnard and Child inequality exercise

Holder inequality Proof Explanation

Estimates with $L^n$ norm

Prove $\sqrt[3]{\frac{(a^4+b^4)(a^4+c^4)(b^4+c^4)}{abc}}\ge \sqrt{\frac{(a^3+bc)(b^3+ca)(c^3+ab)}{1+abc}}$

Find an upper bound on the expectation of squared norm given an upper bound on the expectation of norm

Inequality with condition $2(x^2+y^2+z^2)\leq 3(x+y+z-1)$

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