Question

Show that $\left|\operatorname{Re}(3+i+2\bar z^2 -iz)\right| \le 6$, when $|z| \le 1$

score 104 · Answer 1 · 2026-04-01 05:07:58

104

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Show that $\left|\operatorname{Re}(3+i+2\bar z^2 -iz)\right| \le 6$, when $|z| \le 1$

Published on 01 Apr 2026 - 5:07

score 83 · Answer 2 · 2026-03-27 05:38:44

83

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A generalisation of a Hardy inequality

Published on 27 Mar 2026 - 5:38

score 200 · Answer 3 · 2018-08-31 18:18:27

200

Views

Prove the inequality and limitation

Published on 31 Aug 2018 - 18:18

score 301 · Answer 4 · 2026-03-26 11:03:13

301

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Prove $\sum\limits_{i=1}^n\frac1{x_i}\sqrt{x_i-x_{i-1}}\le\sum\limits_{i=1}^{n^2}\frac1i-\frac12$ for integers $1=x_0\le x_1\le x_2\le\cdots\le x_n$

Published on 26 Mar 2026 - 11:03

score 35 · Answer 5 · 2018-09-01 05:21:08

35

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Using an inequality on derivative of a function to arrive at an inequality on the function

Published on 01 Sep 2018 - 5:21

score 79 · Answer 6 · 2018-09-01 06:54:51

79

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Prove that $a+b+c\le 0$

Published on 01 Sep 2018 - 6:54

score 146 · Answer 7 · 2018-09-01 12:27:46

146

Views

Show that $f(x)=x^r+r^x$ is increasing

Published on 01 Sep 2018 - 12:27

score 86 · Answer 8 · 2026-03-26 03:01:47

86

Views

Prove this inequality for given conditions

Published on 26 Mar 2026 - 3:01

score 108 · Answer 9 · 2026-03-27 23:23:31

108

Views

Inequality $|\exp(i \xi \cdot x) - \exp(i \xi \cdot y) | \leq C |x-y|^\alpha |\xi|^\alpha,$

Published on 27 Mar 2026 - 23:23

score 573 · Answer 10 · 2026-04-06 22:42:04

573

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Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$

Published on 06 Apr 2026 - 22:42

score 121 · Answer 11 · 2026-03-26 03:08:20

121

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Maximizing $x^2 y + y^2 z + z^2 x − x^2 z − y^2 x − z^2 y$ for $x$, $y$, $z$ between $0$ and $1$ (inclusive)

Published on 26 Mar 2026 - 3:08

score 210 · Answer 12 · 2018-09-02 22:17:30

210

Views

Strengthened inequalities

Published on 02 Sep 2018 - 22:17

score 2.5k · Answer 13 · 2018-09-03 02:55:35

2.5k

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If $f(x)<g(x)$, can $\int_a^b f(x)\,dx = \int_a^b g(x)\,dx$?

Published on 03 Sep 2018 - 2:55

score 116 · Answer 14 · 2026-03-25 17:40:47

116

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Finding the values of $x$ and $y$ for which $x^2 + y^2$ is a minimum

Published on 25 Mar 2026 - 17:40

score 120 · Answer 15 · 2026-03-30 08:15:00

120

Views

$c{\lvert}{\rvert}x{\lvert}{\rvert}_\infty \le {\lvert}{\rvert}x{\lvert}{\rvert}_2 \le C{\lvert}{\rvert}x{\lvert}{\rvert}_\infty$?

Published on 30 Mar 2026 - 8:15

List Question

Show that $\left|\operatorname{Re}(3+i+2\bar z^2 -iz)\right| \le 6$, when $|z| \le 1$

A generalisation of a Hardy inequality

Prove the inequality and limitation

Prove $\sum\limits_{i=1}^n\frac1{x_i}\sqrt{x_i-x_{i-1}}\le\sum\limits_{i=1}^{n^2}\frac1i-\frac12$ for integers $1=x_0\le x_1\le x_2\le\cdots\le x_n$

Using an inequality on derivative of a function to arrive at an inequality on the function

Prove that $a+b+c\le 0$

Show that $f(x)=x^r+r^x$ is increasing

Prove this inequality for given conditions

Inequality $|\exp(i \xi \cdot x) - \exp(i \xi \cdot y) | \leq C |x-y|^\alpha |\xi|^\alpha,$

Prove that if $a+b+c+d=4$, then $(a^2+3)(b^2+3)(c^2+3)(d^2+3)\geq256$

Maximizing $x^2 y + y^2 z + z^2 x − x^2 z − y^2 x − z^2 y$ for $x$, $y$, $z$ between $0$ and $1$ (inclusive)

Strengthened inequalities

If $f(x)<g(x)$, can $\int_a^b f(x)\,dx = \int_a^b g(x)\,dx$?

Finding the values of $x$ and $y$ for which $x^2 + y^2$ is a minimum

$c{\lvert}{\rvert}x{\lvert}{\rvert}_\infty \le {\lvert}{\rvert}x{\lvert}{\rvert}_2 \le C{\lvert}{\rvert}x{\lvert}{\rvert}_\infty$?

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