List questions from integral-inequality

53

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Show that $ \frac{2+\ln a }{2}\lt\frac{a-1}{\ln a} \lt \frac{1+a}{2}$ becomes $ \frac{2(a-1)}{a+1}\lt\ln a \lt -1 + \sqrt{2a-1}$

Published on 08 Aug 2014 - 4:56

2.4k

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Inequality of integrals $\int_0^1(f(x))^2 dx \geq 4$ if $\int_0^1xf(x) dx=\int_0^1f(x) dx = 1$

Published on 10 Aug 2014 - 17:59

39

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Lower bound on $F$ under the assumption $\theta F(s)\le sF'(s)$

Published on 21 Aug 2014 - 16:36

297

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A false integral inequality

Published on 25 Aug 2014 - 17:15

441

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Inequality of numerical integration $\int _0^\infty x^{-x}\,dx$.

Published on 26 Aug 2014 - 10:43

100

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How prove this integral inequality$ \int_{0}^{+\infty}\frac{1}{x^x}{\rm d}x<2 $

Published on 27 Aug 2014 - 3:50

352

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An Integral Inequality

Published on 02 Sep 2014 - 16:06

118

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Integral Inequality involving the Euclidian Norm

Published on 06 Sep 2014 - 16:37

80

Views

$L_2$ error between a non-negative monotone function and its mean?

Published on 07 Sep 2014 - 10:47

301

Views

Upperbound for integral of a function times a cosine

Published on 09 Sep 2014 - 13:20

130

Views

Inequality with definite integrals

Published on 12 Sep 2014 - 9:44

51

Views

Integral mean inequalities

Published on 14 Sep 2014 - 6:01

1.5k

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Maximal inequality for a sequence of partial sums of independent random variables

Published on 21 Sep 2014 - 12:42

190

Views

L^2 space convolution inequality

Published on 22 Sep 2014 - 2:50

185

Views

How can Use Gronwall for this PDE?

Published on 02 Oct 2014 - 19:02

List Question

Show that $ \frac{2+\ln a }{2}\lt\frac{a-1}{\ln a} \lt \frac{1+a}{2}$ becomes $ \frac{2(a-1)}{a+1}\lt\ln a \lt -1 + \sqrt{2a-1}$

Inequality of integrals $\int_0^1(f(x))^2 dx \geq 4$ if $\int_0^1xf(x) dx=\int_0^1f(x) dx = 1$

Lower bound on $F$ under the assumption $\theta F(s)\le sF'(s)$

A false integral inequality

Inequality of numerical integration $\int _0^\infty x^{-x}\,dx$.

How prove this integral inequality$ \int_{0}^{+\infty}\frac{1}{x^x}{\rm d}x<2 $

An Integral Inequality

Integral Inequality involving the Euclidian Norm

$L_2$ error between a non-negative monotone function and its mean?

Upperbound for integral of a function times a cosine

Inequality with definite integrals

Integral mean inequalities

Maximal inequality for a sequence of partial sums of independent random variables

L^2 space convolution inequality

How can Use Gronwall for this PDE?

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