List questions from inequality

Published on 12 Apr 2026 - 23:17

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Equality case in Hölder's inequality

Published on 13 Apr 2026 - 5:58

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Show that $\int_{0}^{\pi/6} {\cos (x^2)}\mathrm{d}x\ge\frac12$.

Published on 25 Mar 2026 - 15:52

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How does $(x-y)^2 \geq 0$ imply $xy ≤ x^2/2 + y^2/2$?

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Sum of positive operators

Published on 08 Apr 2026 - 23:02

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Bound from below for the power of the sum of two positive operators

Published on 11 Apr 2026 - 0:30

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Is right the inequality: $|a|+|b| \leq 2|a+ib|$

Published on 13 Apr 2026 - 5:14

46

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Proof about inequalities

Published on 11 Apr 2026 - 4:08

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Show $||f||_p\leq ||f||_\infty$

Published on 29 Mar 2026 - 13:41

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Prove $\sin^{-1}(1)\geq \int_0^b1/\sqrt{1-x^2}dx +(1-b)\pi/2$ for $b \in [0,1)$

Published on 11 Dec 2018 - 17:39

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Show that the functional $F$ on $L_p(-1,1)$ given by $ F(f) = \int_{-1}^0 f(t)dt - \int_{0}^1 f(t)dt $ is continuous.

Published on 29 Mar 2026 - 13:40

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Prove the sequence $a_{1} = 4$, $a_{n + 1} = \frac{a_{n}}{2} + \frac{2}{a_{n}}$, $n = 1, 2, \ldots$ satisfies $a_{n} > 2$

Published on 25 Mar 2026 - 19:06

56

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Proof of $2^n > n$ by Induction

Published on 12 Apr 2026 - 21:16

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How to prove $ \sqrt { \frac {s(c-a-b)}{2∆} } $ is equal to i?

Published on 08 Apr 2026 - 23:21

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A simple proof for $\prod_{i=1}^d a_i+\prod_{i=1}^d b_i \le \prod_{i=1}^d (a_i^d+b_i^d)^{1/d}$?

Published on 25 Mar 2026 - 3:21

List Question

Normed linear space

Equality case in Hölder's inequality

Show that $\int_{0}^{\pi/6} {\cos (x^2)}\mathrm{d}x\ge\frac12$.

How does $(x-y)^2 \geq 0$ imply $xy ≤ x^2/2 + y^2/2$?

Sum of positive operators

Bound from below for the power of the sum of two positive operators

Is right the inequality: $|a|+|b| \leq 2|a+ib|$

Proof about inequalities

Show $||f||_p\leq ||f||_\infty$

Prove $\sin^{-1}(1)\geq \int_0^b1/\sqrt{1-x^2}dx +(1-b)\pi/2$ for $b \in [0,1)$

Show that the functional $F$ on $L_p(-1,1)$ given by $ F(f) = \int_{-1}^0 f(t)dt - \int_{0}^1 f(t)dt $ is continuous.

Prove the sequence $a_{1} = 4$, $a_{n + 1} = \frac{a_{n}}{2} + \frac{2}{a_{n}}$, $n = 1, 2, \ldots$ satisfies $a_{n} > 2$

Proof of $2^n > n$ by Induction

How to prove $ \sqrt { \frac {s(c-a-b)}{2∆} } $ is equal to i?

A simple proof for $\prod_{i=1}^d a_i+\prod_{i=1}^d b_i \le \prod_{i=1}^d (a_i^d+b_i^d)^{1/d}$?

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