Question

Non-decreasing functions satisfying functional inequalities $f(1+ax)\leq a f(1+x)$ and $f(xy)\leq f(x)+f(y)$

score 47 · Answer 1 · 2026-03-25 21:59:49

47

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Non-decreasing functions satisfying functional inequalities $f(1+ax)\leq a f(1+x)$ and $f(xy)\leq f(x)+f(y)$

Published on 25 Mar 2026 - 21:59

score 29 · Answer 2 · 2026-03-25 12:00:37

29

Views

Gradient of a radial function

Published on 25 Mar 2026 - 12:00

score 127 · Answer 3 · 2026-03-25 21:06:30

127

Views

Trigonometric inequality $|\sin{a_1}|+|\sin{a_2}|+...+|\sin{a_n}|+|\cos{(a_1+a_2+...+a_n)}| \ge1$ for all real $a_i$

Published on 25 Mar 2026 - 21:06

score 63 · Answer 4 · 2026-03-25 00:33:14

63

Views

The functional inequality $f(|x|)+f(|y|) \geq 1/f(|x+y|)$

Published on 25 Mar 2026 - 0:33

score 541 · Answer 5 · 2026-03-25 10:22:18

541

Views

Improving the inequality $x\sigma_1(x) \leq \sigma_1(x^2)$ for $x \in \mathbb{N}$

Published on 25 Mar 2026 - 10:22

score 778 · Answer 6 · 2026-03-26 05:39:14

778

Views

Sketch $ z\in \mathbb{C}:0 < arg(z-(1+i)) < \frac\pi3 $

Published on 26 Mar 2026 - 5:39

score 166 · Answer 7 · 2026-03-25 00:19:37

166

Views

Inequality About $f(t)=\int_{0}^t \sqrt{\cos(x)} dx$

Published on 25 Mar 2026 - 0:19

score 163 · Answer 8 · 2026-03-25 06:55:25

163

Views

Proving $\frac{p_{n+1}^2-p_{n+1}^{-C}}{p_{n+1}^2-1}>\frac{f(n) p_n \log p_n }{p_{n+1} \log p_{n+1}},$ where $f(n)\to1$, for some constant $C>1$

Published on 25 Mar 2026 - 6:55

score 68 · Answer 9 · 2026-03-25 22:35:30

68

Views

$ \int_{\mathbb R^d}\int_{\mathbb R^d}b(x,y)\,f(x)\,f(y)dx\,dy \leq ||b_+||_{L^2(\mathbb R^d\times \mathbb R^d)}||f||_{L^2(\mathbb R^d)}^2 $

Published on 25 Mar 2026 - 22:35

score 90 · Answer 10 · 2026-03-25 04:32:19

90

Views

A functional inequality

Published on 25 Mar 2026 - 4:32

score 92 · Answer 11 · 2026-03-25 08:34:13

92

Views

Estimating distance between two functions

Published on 25 Mar 2026 - 8:34

score 211 · Answer 12 · 2026-03-26 04:42:34

211

Views

If $\int_{[0,1]} x^k f(x) dx =1$ then $\int_{[0,1]} (f(x))^2 dx \ge n^2$

Published on 26 Mar 2026 - 4:42

score 121 · Answer 13 · 2026-03-26 01:47:32

121

Views

If $\,\,f:[a,b]\to \mathbb{R}, \,b-a\ge 4$, is differentiable, then $\,f'(x_0)<1+(\,f(x_0))^2$, for some $x_0\in (a,b)$.

Published on 26 Mar 2026 - 1:47

score 165 · Answer 14 · 2026-03-26 00:33:14

165

Views

For a random variable $X$ such that $P(a<X<b)=1$, showing $E(X)E\left(\frac{1}{X}\right) \le\frac{(a+b)^2}{4ab}$

Published on 26 Mar 2026 - 0:33

score 1.1k · Answer 15 · 2026-03-25 16:34:38

1.1k

Views

Numerical methods to solve nonlinear system of inequalities?

Published on 25 Mar 2026 - 16:34

List Question

Non-decreasing functions satisfying functional inequalities $f(1+ax)\leq a f(1+x)$ and $f(xy)\leq f(x)+f(y)$

Gradient of a radial function

Trigonometric inequality $|\sin{a_1}|+|\sin{a_2}|+...+|\sin{a_n}|+|\cos{(a_1+a_2+...+a_n)}| \ge1$ for all real $a_i$

The functional inequality $f(|x|)+f(|y|) \geq 1/f(|x+y|)$

Improving the inequality $x\sigma_1(x) \leq \sigma_1(x^2)$ for $x \in \mathbb{N}$

Sketch $ z\in \mathbb{C}:0 < arg(z-(1+i)) < \frac\pi3 $

Inequality About $f(t)=\int_{0}^t \sqrt{\cos(x)} dx$

Proving $\frac{p_{n+1}^2-p_{n+1}^{-C}}{p_{n+1}^2-1}>\frac{f(n) p_n \log p_n }{p_{n+1} \log p_{n+1}},$ where $f(n)\to1$, for some constant $C>1$

$ \int_{\mathbb R^d}\int_{\mathbb R^d}b(x,y)\,f(x)\,f(y)dx\,dy \leq ||b_+||_{L^2(\mathbb R^d\times \mathbb R^d)}||f||_{L^2(\mathbb R^d)}^2 $

A functional inequality

Estimating distance between two functions

If $\int_{[0,1]} x^k f(x) dx =1$ then $\int_{[0,1]} (f(x))^2 dx \ge n^2$

If $\,\,f:[a,b]\to \mathbb{R}, \,b-a\ge 4$, is differentiable, then $\,f'(x_0)<1+(\,f(x_0))^2$, for some $x_0\in (a,b)$.

For a random variable $X$ such that $P(a<X<b)=1$, showing $E(X)E\left(\frac{1}{X}\right) \le\frac{(a+b)^2}{4ab}$

Numerical methods to solve nonlinear system of inequalities?

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