List questions from integral-inequality

56

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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 16 Apr 2026 - 1:50

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 17 Apr 2026 - 10:56

42

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

Published on 15 Apr 2026 - 10:40

300

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A false integral inequality

Published on 09 Apr 2026 - 17:25

444

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

Published on 15 Apr 2026 - 20:19

103

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

Published on 16 Apr 2026 - 11:35

355

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An Integral Inequality

Published on 09 Apr 2026 - 8:34

121

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Integral Inequality involving the Euclidian Norm

Published on 11 Apr 2026 - 6:19

83

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

Published on 11 Apr 2026 - 2:56

304

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Upperbound for integral of a function times a cosine

Published on 11 Apr 2026 - 23:54

133

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Inequality with definite integrals

Published on 10 Apr 2026 - 16:12

54

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Integral mean inequalities

Published on 10 Apr 2026 - 10:24

1.5k

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

Published on 13 Apr 2026 - 1:39

193

Views

L^2 space convolution inequality

Published on 17 Apr 2026 - 15:44

188

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How can Use Gronwall for this PDE?

Published on 11 Apr 2026 - 19:47

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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