Question

How to prove $ \sum a_ib_ic_i\leq \left(\sum a_i^2\right)^{1/2}\left(\sum b_i^2\right)^{1/2}\left(\sum c_i^2\right)^{1/2} $ with $a_i,b_i,c_i\geq 0$?

score 445 · Answer 1 · 2016-10-29 15:53:25

How to prove $ \sum a_ib_ic_i\leq \left(\sum a_i^2\right)^{1/2}\left(\sum b_i^2\right)^{1/2}\left(\sum c_i^2\right)^{1/2} $ with $a_i,b_i,c_i\geq 0$?

score 645 · Answer 2 · 2016-10-31 12:26:11

645

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362

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score 126 · Answer 5 · 2016-11-07 06:32:22

126

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score 149 · Answer 6 · 2016-11-14 15:36:50

149

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score 153 · Answer 7 · 2016-11-15 23:43:42

153

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543

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score 219 · Answer 11 · 2016-12-02 18:53:39

219

Views

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score 183 · Answer 12 · 2016-12-03 13:13:53

Why is $|f|_{L^p}\le|f|^{\frac 1p}_{L^1}|f|^{\frac 1q}_{L^{\infty}}$ or in general $|f|_{L^p}\le|f|^{\frac 1p}_{L^{p'}}|f|^{\frac 1q}_{L^{q'}}$

score 190 · Answer 13 · 2016-12-08 18:15:52

190

Views

$|f(\frac{1}{2})|\leq \int_{0}^{1}|f(t)|dt+\frac{1}{2}\int_{0}^{1}|f'(t)|dt$

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score 72 · Answer 14 · 2016-12-12 23:26:54

72

Views

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score 167 · Answer 15 · 2016-12-15 02:11:00

167

Views

Inequality of continuous functions with integral

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List Question

How to prove $ \sum a_ib_ic_i\leq \left(\sum a_i^2\right)^{1/2}\left(\sum b_i^2\right)^{1/2}\left(\sum c_i^2\right)^{1/2} $ with $a_i,b_i,c_i\geq 0$?

Prove the Integral Inequality.

A question on Integral inequality

Boundedness of integral

Prove $f(x)\le0$ if $f(0)=0$ and $\int_0^xf(t)\mathbb dt\ge xf(x)$

Trigonometric Integral Estimate

$x+y+z+4xyz=2$ prove that$ xy+yz+xz\le 1$

A question on an integral inequality (Cauchy - Schwartz)

On a Clarkson-like inequality in $L^p$

Prove an inequality on $L^p$ space. Looks like Markov inequality, but not

Which continuous function satisfies $\int\limits_0^x f(t) dt \ge f(x)$ for all $x$ in $[0,1] $?

Why is $|f|_{L^p}\le|f|^{\frac 1p}_{L^1}|f|^{\frac 1q}_{L^{\infty}}$ or in general $|f|_{L^p}\le|f|^{\frac 1p}_{L^{p'}}|f|^{\frac 1q}_{L^{q'}}$

$|f(\frac{1}{2})|\leq \int_{0}^{1}|f(t)|dt+\frac{1}{2}\int_{0}^{1}|f'(t)|dt$

Show that $\int_0^A (A-x) \cos(x) \ f(x) dx \ge 0$ for $f(x)$ monotone decreasing, non-negative and bounded.

Inequality of continuous functions with integral

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