List questions from integral-inequality

Published on 15 Dec 2012 - 16:25

138

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How to prove the first inequality?

Published on 27 Dec 2012 - 9:39

628

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When is Hardy's inequality a strict inequality?

Published on 27 Dec 2012 - 14:52

237

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Prove that $\int_0^1f(x)dx$$\int_0^1g(x)dx\ge1$.

Published on 05 Jan 2013 - 21:32

819

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Do inequalities that hold for infinite sums hold for integrals too?

Published on 07 Jan 2013 - 8:23

392

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A variation of Jensens inequality .

Published on 08 Jan 2013 - 19:47

2.1k

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Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$

Published on 13 Jan 2013 - 4:19

578

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integration inequality

Published on 15 Jan 2013 - 4:20

189

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Inequalities of integrals of periodic functions

Published on 17 Jan 2013 - 20:08

155

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How to asymptotically estimate a lower bound of this function?

Published on 18 Jan 2013 - 3:33

252

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Given $\int_0^1 x f(x)dx=0$, show that $\int_0^1|1-f(x)|dx>1/2$

Published on 08 Feb 2013 - 15:40

2k

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Holder's inequality for infinite products

Published on 19 Feb 2013 - 2:23

138

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Need to prove $\frac{3}{5}(2^{\frac{1}{3}}-1)\le\int_0^1\frac{x^4}{(1+x^6)^{\frac{2}{3}}}dx\le1$

Published on 24 Feb 2013 - 9:18

428

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$3\int_{0}^{1}(f'(x))^2dx \geq (2\int_{0}^{1}f(x)dx)^2 \impliedby 2\int_{0}^{\frac{1}{2}}f(x)\,\mathrm dx=\int_{\frac{1}{2}}^{1}f(x) \,\mathrm dx$

Published on 01 Mar 2013 - 20:34

245

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integer Random Walk with step size governed by a distribution.

Published on 19 Mar 2013 - 6:54

List Question

An inequality from the handbook of mathematical functions (by Abramowitz and Stegun)

How to prove the first inequality?

When is Hardy's inequality a strict inequality?

Prove that $\int_0^1f(x)dx$$\int_0^1g(x)dx\ge1$.

Do inequalities that hold for infinite sums hold for integrals too?

A variation of Jensens inequality .

Prove the following integral inequality: $\int_{0}^{1}f(g(x))dx\le\int_{0}^{1}f(x)dx+\int_{0}^{1}g(x)dx$

integration inequality

Inequalities of integrals of periodic functions

How to asymptotically estimate a lower bound of this function?

Given $\int_0^1 x f(x)dx=0$, show that $\int_0^1|1-f(x)|dx>1/2$

Holder's inequality for infinite products

Need to prove $\frac{3}{5}(2^{\frac{1}{3}}-1)\le\int_0^1\frac{x^4}{(1+x^6)^{\frac{2}{3}}}dx\le1$

$3\int_{0}^{1}(f'(x))^2dx \geq (2\int_{0}^{1}f(x)dx)^2 \impliedby 2\int_{0}^{\frac{1}{2}}f(x)\,\mathrm dx=\int_{\frac{1}{2}}^{1}f(x) \,\mathrm dx$

integer Random Walk with step size governed by a distribution.

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