List questions from functional-inequalities

Published on 07 Sep 2020 - 20:44

150

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Find the upper bound of Square of Sum in fractional form?

Published on 08 Sep 2020 - 8:53

277

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Poincaré inequality on a dilated ball

Published on 10 Sep 2020 - 11:30

45

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Behavior of the Sum $\sum_{n=0}^{\lfloor \sqrt{x} \rfloor} \left( \lfloor \sqrt{x+kx^{1/4}-a^2} \rfloor - \lfloor \sqrt{x-a^2} \rfloor \right)$

Published on 16 Sep 2020 - 8:24

55

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When $f(x)f(y) \le f(xy)$ holds?

Published on 16 Sep 2020 - 11:32

148

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Prove that identity function is a global minimum of a symmetric and quadratic functional

Published on 26 Sep 2020 - 21:07

129

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Proving inequality using Taylor polynomial of arctan

Published on 06 Oct 2020 - 21:59

33

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Is it possible to build any condition on $x,y,z \in \Bbb R$ for $x\log(x)+y\log(y)<2z\log(z)$?

Published on 25 Oct 2020 - 13:40

48

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In this solution, can someone please explain why we are allowed to substitute b=2f(a)?

Published on 26 Oct 2020 - 1:12

61

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Is it true that $D_{KL}[q_1 \| p]\leq D_{KL}[q_2 \| p] \Rightarrow D_{KL}[p\|q_1]\leq D_{KL}[p \| q_2]$?

Published on 23 Feb 2026 - 11:51

222

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Find a continuous function such that$f:\mathbb{R}\to \mathbb{R}$, $f(0)=0$ and $f(2x)\geq x+f(x)$ and $f(3x)\leq 2x+f(x)$.

Published on 28 Oct 2020 - 19:41

73

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Is the following inequality correct and how to prove it?

Published on 14 Nov 2020 - 7:54

71

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A differential inequality of the first order

Published on 20 Nov 2020 - 3:06

232

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Prove $\inf{f+g} \ge \inf{f}+\inf{g}$

Published on 22 Nov 2020 - 17:06

101

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Cyclic inequality with fractions

Published on 05 Dec 2020 - 23:19

List Question

Existence of exotic Point-Halfspace duality?

Find the upper bound of Square of Sum in fractional form?

Poincaré inequality on a dilated ball

Behavior of the Sum $\sum_{n=0}^{\lfloor \sqrt{x} \rfloor} \left( \lfloor \sqrt{x+kx^{1/4}-a^2} \rfloor - \lfloor \sqrt{x-a^2} \rfloor \right)$

When $f(x)f(y) \le f(xy)$ holds?

Prove that identity function is a global minimum of a symmetric and quadratic functional

Proving inequality using Taylor polynomial of arctan

Is it possible to build any condition on $x,y,z \in \Bbb R$ for $x\log(x)+y\log(y)<2z\log(z)$?

In this solution, can someone please explain why we are allowed to substitute b=2f(a)?

Is it true that $D_{KL}[q_1 \| p]\leq D_{KL}[q_2 \| p] \Rightarrow D_{KL}[p\|q_1]\leq D_{KL}[p \| q_2]$?

Find a continuous function such that$f:\mathbb{R}\to \mathbb{R}$, $f(0)=0$ and $f(2x)\geq x+f(x)$ and $f(3x)\leq 2x+f(x)$.

Is the following inequality correct and how to prove it?

A differential inequality of the first order

Prove $\inf{f+g} \ge \inf{f}+\inf{g}$

Cyclic inequality with fractions

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