Question

Given three positive numbers $a,b,c$. Prove that $\prod\limits_{sym}(\!a+\frac{1}{a}\!)\geqq\frac{4}{3}\sum\limits_{sym}\frac{b+c}{a}$ .

score 203 · Answer 1 · 2026-03-24 22:08:44

203

Views

Given three positive numbers $a,b,c$. Prove that $\prod\limits_{sym}(\!a+\frac{1}{a}\!)\geqq\frac{4}{3}\sum\limits_{sym}\frac{b+c}{a}$ .

Published on 24 Mar 2026 - 22:08

score 105 · Answer 2 · 2019-05-14 14:57:35

105

Views

Inequality between two sums

Published on 14 May 2019 - 14:57

score 297 · Answer 3 · 2026-03-25 06:07:04

297

Views

Given three positve numbers $a,b,c$. Prove that $\sum\limits_{cyc}\frac{a}{\sqrt{b(a+b)}}\geqq \sum\limits_{cyc}\frac{a}{\sqrt{b(c+a)}}$ .

Published on 25 Mar 2026 - 6:07

score 152 · Answer 4 · 2019-05-29 13:54:49

152

Views

Holder unsuccessful here!

Published on 29 May 2019 - 13:54

score 77 · Answer 5 · 2019-06-06 03:22:24

77

Views

Unclear Use of Holder`s Inequality

Published on 06 Jun 2019 - 3:22

score 113 · Answer 6 · 2019-06-12 23:47:33

113

Views

$L^p$ norm inequality for measurable function

Published on 12 Jun 2019 - 23:47

score 137 · Answer 7 · 2019-06-13 20:40:10

137

Views

Trouble with Holder Inequality Gymnastics: $\left(\int fg^{q}\right)^{r-p}\leq\left(\int fg^p\right)^{r-q}\left(\int fg^r\right)^{q-p}.$

Published on 13 Jun 2019 - 20:40

score 70 · Answer 8 · 2019-06-20 15:36:25

70

Views

Prove that inequality $27+7\left(ab+bc+ca\right)\le 8\left(\sum \sqrt{a+3b}\right)$

Published on 20 Jun 2019 - 15:36

score 211 · Answer 9 · 2019-06-23 17:09:36

211

Views

Is it true that a sequence $ f_n \to f $ of measurable functions is bounded by a norm of $ L^p $ then $ f_n $ converges to $f$ in $ L^p $?

Published on 23 Jun 2019 - 17:09

score 90 · Answer 10 · 2019-06-30 09:27:55

90

Views

Inequality of integral : $\int_0^{1}((\sqrt{3}f(x))^{2}-2(f(x)^{3})dx≤1$

Published on 30 Jun 2019 - 9:27

score 183 · Answer 11 · 2026-03-25 06:13:00

183

Views

$\frac{3(a + b + c)^2}{25(ab + bc + ca)(a^2 + b^2 + c^2)} \le \sum_{cyc}\frac{1}{(3a + b + c)(c + 4a)} \le \frac{\sqrt{3(ab + bc + ca)}}{25abc}$

Published on 25 Mar 2026 - 6:13

score 110 · Answer 12 · 2019-07-03 08:42:12

110

Views

Prove the inequality of integral using Hölder

Published on 03 Jul 2019 - 8:42

score 306 · Answer 13 · 2019-07-07 13:38:55

306

Views

If $D$ is bounded and $f$ is $\alpha$-Hölder continuous, then $f$ is also $\beta$-Hölder continuous for $\beta \in (0,\alpha]$

Published on 07 Jul 2019 - 13:38

score 137 · Answer 14 · 2019-07-08 15:59:52

137

Views

Show that $\sum_{cyc} \sqrt{8a+b^3}\ge 9$

Published on 08 Jul 2019 - 15:59

score 83 · Answer 15 · 2019-07-09 17:00:35

83

Views

Inequality in triangle $ABC$ $a=BC$ $b=AC$ $c=AB$

Published on 09 Jul 2019 - 17:00

List Question

Given three positive numbers $a,b,c$. Prove that $\prod\limits_{sym}(\!a+\frac{1}{a}\!)\geqq\frac{4}{3}\sum\limits_{sym}\frac{b+c}{a}$ .

Inequality between two sums

Given three positve numbers $a,b,c$. Prove that $\sum\limits_{cyc}\frac{a}{\sqrt{b(a+b)}}\geqq \sum\limits_{cyc}\frac{a}{\sqrt{b(c+a)}}$ .

Holder unsuccessful here!

Unclear Use of Holder`s Inequality

$L^p$ norm inequality for measurable function

Trouble with Holder Inequality Gymnastics: $\left(\int fg^{q}\right)^{r-p}\leq\left(\int fg^p\right)^{r-q}\left(\int fg^r\right)^{q-p}.$

Prove that inequality $27+7\left(ab+bc+ca\right)\le 8\left(\sum \sqrt{a+3b}\right)$

Is it true that a sequence $ f_n \to f $ of measurable functions is bounded by a norm of $ L^p $ then $ f_n $ converges to $f$ in $ L^p $?

Inequality of integral : $\int_0^{1}((\sqrt{3}f(x))^{2}-2(f(x)^{3})dx≤1$

$\frac{3(a + b + c)^2}{25(ab + bc + ca)(a^2 + b^2 + c^2)} \le \sum_{cyc}\frac{1}{(3a + b + c)(c + 4a)} \le \frac{\sqrt{3(ab + bc + ca)}}{25abc}$

Prove the inequality of integral using Hölder

If $D$ is bounded and $f$ is $\alpha$-Hölder continuous, then $f$ is also $\beta$-Hölder continuous for $\beta \in (0,\alpha]$

Show that $\sum_{cyc} \sqrt{8a+b^3}\ge 9$

Inequality in triangle $ABC$ $a=BC$ $b=AC$ $c=AB$

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