Question

show $a^2 + b^2 + c^2 = 12 \implies a\sqrt[3]{b^2 + c^2} + b\sqrt[3]{c^2 + a^2} + c\sqrt[3]{a^2 + b^2} \le 12$

score 88 · Answer 1 · 2023-08-05 16:10:54

88

Views

show $a^2 + b^2 + c^2 = 12 \implies a\sqrt[3]{b^2 + c^2} + b\sqrt[3]{c^2 + a^2} + c\sqrt[3]{a^2 + b^2} \le 12$

Published on 05 Aug 2023 - 16:10

score 79 · Answer 2 · 2023-08-07 07:48:07

79

Views

Let $x+y+z=1$, $x,y,z> 0$. Show that $\sum_{cyc}\sqrt{1-2xy}\geq\sqrt7$ by Jensen's inequality?

Published on 07 Aug 2023 - 7:48

score 84 · Answer 3 · 2023-08-07 14:02:09

84

Views

Prove $\int_{\Omega} |u|^2 dx \le c\int_{\Omega} e^{|u|^2} dx$ through Hölder inequality

Published on 07 Aug 2023 - 14:02

score 135 · Answer 4 · 2023-08-08 04:28:01

135

Views

Minimize $\sum_{cyc}\sqrt{\frac{a+b+1}{c+ab}}$ if $ab+bc+ca=1.$

Published on 08 Aug 2023 - 4:28

score 158 · Answer 5 · 2023-08-09 03:34:09

158

Views

Prove $\sum\limits_{\mathrm{cyc}} \frac{4a+1}{\sqrt{4a+bc}}\ge 6$ for $a, b, c \ge 0$ with $ab+bc+ca=1$

Published on 09 Aug 2023 - 3:34

score 201 · Answer 6 · 2023-08-09 13:36:01

201

Views

How to prove $\frac{1}{\sqrt{2a^2+2bc+17}}+\frac{1}{\sqrt{2b^2+2ca+17}}+\frac{1}{\sqrt{2c^2+2ab+17}}\le \frac{\sqrt{21}}{7}$

Published on 09 Aug 2023 - 13:36

score 110 · Answer 7 · 2023-08-10 08:24:28

110

Views

Prove $\frac{1}{\sqrt{4a+4b+1}}+\frac{1}{\sqrt{4c+4b+1}}+\frac{1}{\sqrt{4a+4c+1}}\ge 1,$ for $ab+bc+ca=abc+2$

Published on 10 Aug 2023 - 8:24

score 266 · Answer 8 · 2023-08-10 10:17:06

266

Views

Inequality Only with Am-Gm

Published on 10 Aug 2023 - 10:17

score 64 · Answer 9 · 2023-08-11 05:46:06

64

Views

How to prove $\frac{1}{a^3+c^3}+\frac{1}{b^3+c^3}+2\left[a+b-c(1-\sqrt{3})\right]\ge3\left(\frac{1}{\sqrt[3]{a+c}}+\frac{1}{\sqrt[3]{b+c}}\right).$?

Published on 11 Aug 2023 - 5:46

score 56 · Answer 10 · 2023-08-23 16:23:18

56

Views

Why if p-th variation is finite, then q-th variation is also finite for q>p?

Published on 23 Aug 2023 - 16:23

score 25 · Answer 11 · 2023-09-18 15:24:45

25

Views

Homogeneous Inequality problem unsolved

Published on 18 Sep 2023 - 15:24

score 437 · Answer 12 · 2023-09-23 10:23:18

437

Views

How to prove $\sqrt{\frac{24a+13}{24a+13bc}}+\sqrt{\frac{24b+13}{24b+13ca}}+\sqrt{\frac{24c+13}{24c+13ab}}\ge 3$

Published on 23 Sep 2023 - 10:23

score 156 · Answer 13 · 2023-09-26 19:13:05

156

Views

Prove $\frac{a}{\sqrt{5-4bc}} + \frac{b}{\sqrt{5-4ac}} + \frac{c}{\sqrt{5-4ab}} \ge 1$ With the condition $a+b+c=3$

Published on 26 Sep 2023 - 19:13

score 67 · Answer 14 · 2023-09-28 13:56:49

67

Views

Holder inequality for 3 functions

Published on 28 Sep 2023 - 13:56

score 42 · Answer 15 · 2023-09-30 07:05:56

42

Views

How to verify ihe Interpolation inequality for the weighted Bessel potential spaces?

Published on 30 Sep 2023 - 7:05

List Question

show $a^2 + b^2 + c^2 = 12 \implies a\sqrt[3]{b^2 + c^2} + b\sqrt[3]{c^2 + a^2} + c\sqrt[3]{a^2 + b^2} \le 12$

Let $x+y+z=1$, $x,y,z> 0$. Show that $\sum_{cyc}\sqrt{1-2xy}\geq\sqrt7$ by Jensen's inequality?

Prove $\int_{\Omega} |u|^2 dx \le c\int_{\Omega} e^{|u|^2} dx$ through Hölder inequality

Minimize $\sum_{cyc}\sqrt{\frac{a+b+1}{c+ab}}$ if $ab+bc+ca=1.$

Prove $\sum\limits_{\mathrm{cyc}} \frac{4a+1}{\sqrt{4a+bc}}\ge 6$ for $a, b, c \ge 0$ with $ab+bc+ca=1$

How to prove $\frac{1}{\sqrt{2a^2+2bc+17}}+\frac{1}{\sqrt{2b^2+2ca+17}}+\frac{1}{\sqrt{2c^2+2ab+17}}\le \frac{\sqrt{21}}{7}$

Prove $\frac{1}{\sqrt{4a+4b+1}}+\frac{1}{\sqrt{4c+4b+1}}+\frac{1}{\sqrt{4a+4c+1}}\ge 1,$ for $ab+bc+ca=abc+2$

Inequality Only with Am-Gm

How to prove $\frac{1}{a^3+c^3}+\frac{1}{b^3+c^3}+2\left[a+b-c(1-\sqrt{3})\right]\ge3\left(\frac{1}{\sqrt[3]{a+c}}+\frac{1}{\sqrt[3]{b+c}}\right).$?

Why if p-th variation is finite, then q-th variation is also finite for q>p?

Homogeneous Inequality problem unsolved

How to prove $\sqrt{\frac{24a+13}{24a+13bc}}+\sqrt{\frac{24b+13}{24b+13ca}}+\sqrt{\frac{24c+13}{24c+13ab}}\ge 3$

Prove $\frac{a}{\sqrt{5-4bc}} + \frac{b}{\sqrt{5-4ac}} + \frac{c}{\sqrt{5-4ab}} \ge 1$ With the condition $a+b+c=3$

Holder inequality for 3 functions

How to verify ihe Interpolation inequality for the weighted Bessel potential spaces?

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