Question

Szegő's inequality in approximation theory

score 113 · Answer 1 · 2021-07-27 14:18:50

Szegő's inequality in approximation theory

Published on 27 Jul 2021 - 14:18

score 86 · Answer 2 · 2021-07-31 12:05:09

If $| f(p + q) – f(q)| \le \dfrac pq$ for all $p$ and $q\in \mathbb Q$ & $q\ne 0$, show that $\sum_{i=1}^k| f(2^k ) – f(2^i ) |\le \dfrac{k(k – 1)}2$

score 444 · Answer 3 · 2021-09-04 07:20:17

444

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Let $f(x)=ax^3+bx^2+cx+5$. If $|f(x)|\le|e^x-e^2|$ for all $x\ge0$ and if the maximum value of $|12a+4b+c|$ is $m$, then find $[m]$

Published on 04 Sep 2021 - 7:20

score 48 · Answer 4 · 2021-09-06 01:18:34

48

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Proper name for a "polytope" when defined by linear functionals

Published on 06 Sep 2021 - 1:18

score 71 · Answer 5 · 2021-09-09 09:43:38

71

Views

Let $f(x)$ satisfies $f(x)\ge|x|^{\alpha}, \frac12\lt\alpha\lt1$ and $f(x)f(2x)\le|x|$ then find $\lim_{x\to0}f(x)$

Published on 09 Sep 2021 - 9:43

score 54 · Answer 6 · 2021-09-14 03:43:20

54

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Why do we consider the lower bound in this Inequality?

Published on 14 Sep 2021 - 3:43

score 56 · Answer 7 · 2021-10-30 18:35:31

56

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Is there a simple proof for $\sup_{|x|\le \delta} \frac{|e^{ax} - 1|}{|x|} \le \frac{e^{|a|\delta}}{\delta}$?

Published on 30 Oct 2021 - 18:35

score 96 · Answer 8 · 2021-11-13 07:35:56

96

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If $f'(x)≥0$, $f''(x)≤0$ then prove that $f(x)f^{-1}(x)-x^2≤0$

Published on 13 Nov 2021 - 7:35

score 85 · Answer 9 · 2021-11-22 00:19:23

85

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How to prove that $f(x)$ is much less than $g(x)$?

Published on 22 Nov 2021 - 0:19

score 72 · Answer 10 · 2021-11-24 16:38:54

72

Views

A problem concerning a divergent function on $[0, 1]$

Published on 24 Nov 2021 - 16:38

score 76 · Answer 11 · 2021-11-25 14:48:41

76

Views

If $f'(x) − f'(y) ≤ 3|x − y|$ then show that $|f(x)−f(y)-f'(y)(x-y)|≤\frac{3}{2}(x-y)^2$

Published on 25 Nov 2021 - 14:48

score 280 · Answer 12 · 2021-12-03 23:14:48

280

Views

Prove Holder's inequality with $0<p<r<q<\infty,\ (1-\theta)/p+\theta/q=1/r$ and $0<\theta<1 \implies \|h\|_r \leq \|h\|_p^{1-\theta} \|h\|_q^{\theta}$

Published on 03 Dec 2021 - 23:14

score 61 · Answer 13 · 2021-12-15 18:24:28

61

Views

2-Normed Space Inequality

Published on 15 Dec 2021 - 18:24

score 107 · Answer 14 · 2021-12-25 14:18:17

107

Views

Deducing Inequality from an Equation

Published on 25 Dec 2021 - 14:18

score 211 · Answer 15 · 2022-01-06 05:08:20

211

Views

If $g(x+y)\le2\cdot\max\{g(x),g(y)\}$ and $g(xy)=g(x)g(y)$, show that $g(x+y)\le g(x)+g(y)$.

Published on 06 Jan 2022 - 5:08

List Question

Szegő's inequality in approximation theory

If $| f(p + q) – f(q)| \le \dfrac pq$ for all $p$ and $q\in \mathbb Q$ & $q\ne 0$, show that $\sum_{i=1}^k| f(2^k ) – f(2^i ) |\le \dfrac{k(k – 1)}2$

Let $f(x)=ax^3+bx^2+cx+5$. If $|f(x)|\le|e^x-e^2|$ for all $x\ge0$ and if the maximum value of $|12a+4b+c|$ is $m$, then find $[m]$

Proper name for a "polytope" when defined by linear functionals

Let $f(x)$ satisfies $f(x)\ge|x|^{\alpha}, \frac12\lt\alpha\lt1$ and $f(x)f(2x)\le|x|$ then find $\lim_{x\to0}f(x)$

Why do we consider the lower bound in this Inequality?

Is there a simple proof for $\sup_{|x|\le \delta} \frac{|e^{ax} - 1|}{|x|} \le \frac{e^{|a|\delta}}{\delta}$?

If $f'(x)≥0$, $f''(x)≤0$ then prove that $f(x)f^{-1}(x)-x^2≤0$

How to prove that $f(x)$ is much less than $g(x)$?

A problem concerning a divergent function on $[0, 1]$

If $f'(x) − f'(y) ≤ 3|x − y|$ then show that $|f(x)−f(y)-f'(y)(x-y)|≤\frac{3}{2}(x-y)^2$

Prove Holder's inequality with $0<p<r<q<\infty,\ (1-\theta)/p+\theta/q=1/r$ and $0<\theta<1 \implies \|h\|_r \leq \|h\|_p^{1-\theta} \|h\|_q^{\theta}$

2-Normed Space Inequality

Deducing Inequality from an Equation

If $g(x+y)\le2\cdot\max\{g(x),g(y)\}$ and $g(xy)=g(x)g(y)$, show that $g(x+y)\le g(x)+g(y)$.

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