Question

Seeking Clarification on an Inequality Involving Roots and Products

score 48 · Answer 1 · 2023-10-13 20:10:40

48

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Seeking Clarification on an Inequality Involving Roots and Products

Published on 13 Oct 2023 - 20:10

score 29 · Answer 2 · 2026-03-25 18:59:06

29

Views

If $f$ is Holder of order $\alpha$, then $f'$ is holder of order $\alpha-1$

Published on 25 Mar 2026 - 18:59

score 45 · Answer 3 · 2023-10-15 17:12:53

45

Views

Proving Inequality Involving Sums and Square Roots with Given Conditions

Published on 15 Oct 2023 - 17:12

score 158 · Answer 4 · 2023-10-21 22:05:32

158

Views

Brazilian Mathematical Olympiad 2023, Level U, Problem 3

Published on 21 Oct 2023 - 22:05

score 138 · Answer 5 · 2023-10-28 17:56:53

138

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Nash Inequality

Published on 28 Oct 2023 - 17:56

score 150 · Answer 6 · 2023-10-29 18:27:30

150

Views

If $a$ and $b$ are positive real numbers such that $a^{2015}+b^{2015}=2015$, find the maximum value of $a+b$.

Published on 29 Oct 2023 - 18:27

score 112 · Answer 7 · 2026-03-26 04:36:27

112

Views

Prove $\sqrt{\frac{a+b}{c+ab}}+\sqrt{\frac{c+b}{a+cb}}+\sqrt{\frac{a+c}{b+ac}}\ge 3,$ if $ab+bc+ca=3.$

Published on 26 Mar 2026 - 4:36

score 60 · Answer 8 · 2023-11-14 09:16:59

60

Views

Hölder's inequality for functions of multiple variables

Published on 14 Nov 2023 - 9:16

score 100 · Answer 9 · 2023-11-14 10:17:13

100

Views

If $f \in L_1(0,1)$, then $f^p \log^q (f) \in L_1(0,1)$.

Published on 14 Nov 2023 - 10:17

score 104 · Answer 10 · 2023-11-18 07:12:17

104

Views

prove that $\frac{1}{a(b + c)^{3}} + \frac{1}{b(c + a)^{3}} + \frac{1}{c(a + b)^{3}} \ge \frac{27}{8}$ given $a^{2} + b^{2} + c^{2} = 1$

Published on 18 Nov 2023 - 7:12

score 88 · Answer 11 · 2023-11-18 15:16:36

88

Views

Prove $\color{black}{\frac{1}{\sqrt{a+b+2}}+\frac{1}{\sqrt{c+b+2}}+\frac{1}{\sqrt{a+c+2}}\ge1+\frac{1}{\sqrt{2(a+b+c-1)}}.}$

Published on 18 Nov 2023 - 15:16

score 39 · Answer 12 · 2023-11-19 17:19:12

39

Views

upper bound over multiplication of two expectation

Published on 19 Nov 2023 - 17:19

score 126 · Answer 13 · 2023-11-21 07:21:32

126

Views

Prove $\color{black}{\sqrt{\frac{7a+2}{b+c}}+\sqrt{\frac{7b+2}{a+c}}+\sqrt{\frac{7c+2}{b+a}}\ge \frac{9\sqrt{2}}{2} },$ if $a+b+c+abc=4.$

Published on 21 Nov 2023 - 7:21

score 78 · Answer 14 · 2023-11-25 04:18:43

78

Views

Finding $\small{\min\limits_{a+b+c=1}P=\sqrt{2a^3+abc}+\sqrt{2b^3+abc}+\sqrt{2c^3+abc}. }$

Published on 25 Nov 2023 - 4:18

score 107 · Answer 15 · 2023-11-26 10:39:35

107

Views

Prove $\sqrt[3]{3a+bc}+\sqrt[3]{3b+ca}+\sqrt[3]{3c+ab}\le \frac{3}{2}\sqrt[3]{a^2+b^2+c^2+29}$ for $ab+bc+ca=3.$

Published on 26 Nov 2023 - 10:39

List Question

Seeking Clarification on an Inequality Involving Roots and Products

If $f$ is Holder of order $\alpha$, then $f'$ is holder of order $\alpha-1$

Proving Inequality Involving Sums and Square Roots with Given Conditions

Brazilian Mathematical Olympiad 2023, Level U, Problem 3

Nash Inequality

If $a$ and $b$ are positive real numbers such that $a^{2015}+b^{2015}=2015$, find the maximum value of $a+b$.

Prove $\sqrt{\frac{a+b}{c+ab}}+\sqrt{\frac{c+b}{a+cb}}+\sqrt{\frac{a+c}{b+ac}}\ge 3,$ if $ab+bc+ca=3.$

Hölder's inequality for functions of multiple variables

If $f \in L_1(0,1)$, then $f^p \log^q (f) \in L_1(0,1)$.

prove that $\frac{1}{a(b + c)^{3}} + \frac{1}{b(c + a)^{3}} + \frac{1}{c(a + b)^{3}} \ge \frac{27}{8}$ given $a^{2} + b^{2} + c^{2} = 1$

Prove $\color{black}{\frac{1}{\sqrt{a+b+2}}+\frac{1}{\sqrt{c+b+2}}+\frac{1}{\sqrt{a+c+2}}\ge1+\frac{1}{\sqrt{2(a+b+c-1)}}.}$

upper bound over multiplication of two expectation

Prove $\color{black}{\sqrt{\frac{7a+2}{b+c}}+\sqrt{\frac{7b+2}{a+c}}+\sqrt{\frac{7c+2}{b+a}}\ge \frac{9\sqrt{2}}{2} },$ if $a+b+c+abc=4.$

Finding $\small{\min\limits_{a+b+c=1}P=\sqrt{2a^3+abc}+\sqrt{2b^3+abc}+\sqrt{2c^3+abc}. }$

Prove $\sqrt[3]{3a+bc}+\sqrt[3]{3b+ca}+\sqrt[3]{3c+ab}\le \frac{3}{2}\sqrt[3]{a^2+b^2+c^2+29}$ for $ab+bc+ca=3.$

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