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 448 · Answer 1 · 2026-04-16 15:42:43

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 648 · Answer 2 · 2026-04-14 15:27:58

648

Views

Prove the Integral Inequality.

Published on 14 Apr 2026 - 15:27

score 39 · Answer 3 · 2026-04-16 20:35:18

39

Views

A question on Integral inequality

Published on 16 Apr 2026 - 20:35

score 365 · Answer 4 · 2026-04-10 18:29:29

365

Views

Boundedness of integral

Published on 10 Apr 2026 - 18:29

score 128 · Answer 5 · 2026-04-15 23:21:27

128

Views

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

Published on 15 Apr 2026 - 23:21

score 152 · Answer 6 · 2026-04-14 00:29:18

152

Views

Trigonometric Integral Estimate

Published on 14 Apr 2026 - 0:29

score 156 · Answer 7 · 2026-04-16 15:00:02

156

Views

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

Published on 16 Apr 2026 - 15:00

score 44 · Answer 8 · 2026-04-12 06:45:14

44

Views

A question on an integral inequality (Cauchy - Schwartz)

Published on 12 Apr 2026 - 6:45

score 539 · Answer 9 · 2026-04-14 10:04:47

539

Views

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

Published on 14 Apr 2026 - 10:04

score 546 · Answer 10 · 2026-04-14 14:32:42

546

Views

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

Published on 14 Apr 2026 - 14:32

score 222 · Answer 11 · 2026-04-15 10:03:07

222

Views

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

Published on 15 Apr 2026 - 10:03

score 186 · Answer 12 · 2026-04-16 23:50:24

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 193 · Answer 13 · 2026-04-17 14:40:22

193

Views

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

Published on 17 Apr 2026 - 14:40

score 75 · Answer 14 · 2026-04-16 06:42:59

75

Views

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

Published on 16 Apr 2026 - 6:42

score 170 · Answer 15 · 2026-04-11 00:02:35

170

Views

Inequality of continuous functions with integral

Published on 11 Apr 2026 - 0:02

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

Trending Questions

Popular # Hahtags

Popular Questions