Question

Prove $\sqrt[3]{a^2+3}+\frac{7}{5\sqrt[3]{14}}\sqrt[3]{b^2+3}+\frac{\sqrt[3]{9}}{5}\sqrt[3]{c^2+3}\ge \frac{23}{5\sqrt[3]{2}}$ given $ab+bc+ca\ge11$

score 131 · Answer 1 · 2017-05-09 12:29:54

131

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Prove $\sqrt[3]{a^2+3}+\frac{7}{5\sqrt[3]{14}}\sqrt[3]{b^2+3}+\frac{\sqrt[3]{9}}{5}\sqrt[3]{c^2+3}\ge \frac{23}{5\sqrt[3]{2}}$ given $ab+bc+ca\ge11$

Published on 09 May 2017 - 12:29

score 264 · Answer 2 · 2017-05-11 13:16:53

264

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Prove: $\frac{a}{m_a}+\frac{b}{m_b}+\frac{c}{m_c}\ge 2\sqrt{3}$

Published on 11 May 2017 - 13:16

score 378 · Answer 3 · 2017-06-21 05:00:42

378

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Proving Cauchy Inequality from Hölder's inequality?

Published on 21 Jun 2017 - 5:00

score 151 · Answer 4 · 2017-06-30 11:30:40

151

Views

Prove this inequality $\sum _{cyc}\frac{a^2}{\sqrt{3b^2+bc}}\ge \frac{3}{2}$

Published on 30 Jun 2017 - 11:30

score 304 · Answer 5 · 2017-07-21 10:22:43

304

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Prove the inequality $\sqrt{\frac{x}{y^2+z^2}}+\sqrt{\frac{y}{z^2+x^2}}+\sqrt{\frac{z}{x^2+y^2}}\ge \frac{2\sqrt{6}}3$ with $x+y+z=3,x,y,z\ge 0$

Published on 21 Jul 2017 - 10:22

score 471 · Answer 6 · 2026-03-26 12:46:23

471

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Prove this trigonometric inequality about the angles of $\triangle ABC$

Published on 26 Mar 2026 - 12:46

score 76 · Answer 7 · 2026-03-26 10:58:19

76

Views

Need help with the following inequality

Published on 26 Mar 2026 - 10:58

score 112 · Answer 8 · 2017-08-05 08:57:54

112

Views

Inequality : $(a^3+3)(b^3+6)(c^3+12)>k(a+b+c)^3$

Published on 05 Aug 2017 - 8:57

score 408 · Answer 9 · 2026-03-26 09:49:58

408

Views

Inequality : $ \sum_{cyc} \frac{a+b}{\sqrt{a+2c}} \geq 2 \sqrt{a+b+c}$

Published on 26 Mar 2026 - 9:49

score 132 · Answer 10 · 2026-02-23 15:03:20

132

Views

Newton method local convergence under Hölder-continuity

Published on 23 Feb 2026 - 15:03

score 1.3k · Answer 11 · 2017-09-04 00:54:17

1.3k

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Proof of Hölder for Lorentz spaces (harmonic analysis)

Published on 04 Sep 2017 - 0:54

score 138 · Answer 12 · 2026-03-25 13:57:05

138

Views

Inequality : $\sum_{cyc}\left(\frac{a^3+1}{a^2+1}\right)^4 \geq \frac{1}{27}\left(\sum_{cyc}\sqrt{ab}\right)^4$

Published on 25 Mar 2026 - 13:57

score 120 · Answer 13 · 2017-09-11 19:38:57

120

Views

application of Holder's inequality 3

Published on 11 Sep 2017 - 19:38

score 217 · Answer 14 · 2017-09-15 16:30:45

217

Views

Prove this inequality $\sum_{cyc}\sqrt{\frac{a}{3b^2+1}}\ge \frac{3}{2}$

Published on 15 Sep 2017 - 16:30

score 48 · Answer 15 · 2017-09-16 17:54:03

48

Views

In $C[(0,1)]$ if $p_1 <p_2$ then $\|{f}\|_{p_1} < \|{f}\|_{p_2}$

Published on 16 Sep 2017 - 17:54

List Question

Prove $\sqrt[3]{a^2+3}+\frac{7}{5\sqrt[3]{14}}\sqrt[3]{b^2+3}+\frac{\sqrt[3]{9}}{5}\sqrt[3]{c^2+3}\ge \frac{23}{5\sqrt[3]{2}}$ given $ab+bc+ca\ge11$

Prove: $\frac{a}{m_a}+\frac{b}{m_b}+\frac{c}{m_c}\ge 2\sqrt{3}$

Proving Cauchy Inequality from Hölder's inequality?

Prove this inequality $\sum _{cyc}\frac{a^2}{\sqrt{3b^2+bc}}\ge \frac{3}{2}$

Prove the inequality $\sqrt{\frac{x}{y^2+z^2}}+\sqrt{\frac{y}{z^2+x^2}}+\sqrt{\frac{z}{x^2+y^2}}\ge \frac{2\sqrt{6}}3$ with $x+y+z=3,x,y,z\ge 0$

Prove this trigonometric inequality about the angles of $\triangle ABC$

Need help with the following inequality

Inequality : $(a^3+3)(b^3+6)(c^3+12)>k(a+b+c)^3$

Inequality : $ \sum_{cyc} \frac{a+b}{\sqrt{a+2c}} \geq 2 \sqrt{a+b+c}$

Newton method local convergence under Hölder-continuity

Proof of Hölder for Lorentz spaces (harmonic analysis)

Inequality : $\sum_{cyc}\left(\frac{a^3+1}{a^2+1}\right)^4 \geq \frac{1}{27}\left(\sum_{cyc}\sqrt{ab}\right)^4$

application of Holder's inequality 3

Prove this inequality $\sum_{cyc}\sqrt{\frac{a}{3b^2+1}}\ge \frac{3}{2}$

In $C[(0,1)]$ if $p_1 <p_2$ then $\|{f}\|_{p_1} < \|{f}\|_{p_2}$

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