User Michael Rozenberg

6 votes

Polynomial inequality of sixth degree

answered Apr 21, 2020 at 1:10

6 votes

Maximal (minimal) value of $S=x_1^2x_2+x_2^2x_3+\cdots+x_{n-1}^2x_n+x_n^2x_1$ on condition that $x_1^2+x_2^2+\cdots+x_n^2=1$

answered Feb 8, 2021 at 17:20

3 votes

Prove that this expression is greater than 1/2

answered Jul 28, 2019 at 8:35

3 votes

How to prove this high-degree inequality

answered Mar 10, 2021 at 11:32

3 votes

Representing a symmetric polynomial as a conical sum of squares

answered May 20, 2021 at 16:09

3 votes

Elementary inhomogeneous inequality for three non-negative reals

answered Nov 6, 2020 at 16:59

2 votes

Algebraic inequalities on different means

answered Jan 26, 2019 at 6:52

2 votes

Accepted

Inequality in a triangle associated with Golden ratio

answered May 16, 2021 at 5:31

1 vote

How to prove this high-degree inequality

answered Mar 10, 2021 at 10:19

1 vote

Wanted: Positivity certificate for the AM-GM inequality in low dimension

answered Jan 30, 2019 at 8:21

1 vote

On the inequality $\sum_{i=1}^nx_i^4\sum_{i=1}^nx_i^2 -\sum_{i=1}^nx_i^6 \leq c\left(\sum_{i=1}^nx_i^3\right)^2$

answered Jan 31, 2019 at 8:46

1 vote

Accepted

Inequality involving product-of-minus vs minus-of-product for positive integers

answered Feb 19, 2019 at 12:05

1 vote

Elementary inhomogeneous inequality for three non-negative reals

answered Nov 6, 2020 at 18:30

1 vote

How to prove that $a + b + 4 \sqrt{1 + a^{2} + b^{2}} \leq 4 \sqrt{a^{2} + b^{2}} + \sqrt{1+b^{2}} + \sqrt{1+a^{2}} + 2 $ for all $a, b > 0$?

answered Nov 10, 2020 at 12:12

0 votes

Given a polynomial constraint equation in $n$ variables, can one conclude that the sum of the variables is non-negative?

answered Sep 21, 2019 at 17:23

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15 Answers

Polynomial inequality of sixth degree

Maximal (minimal) value of $S=x_1^2x_2+x_2^2x_3+\cdots+x_{n-1}^2x_n+x_n^2x_1$ on condition that $x_1^2+x_2^2+\cdots+x_n^2=1$

Prove that this expression is greater than 1/2

How to prove this high-degree inequality

Representing a symmetric polynomial as a conical sum of squares

Elementary inhomogeneous inequality for three non-negative reals

Algebraic inequalities on different means

Inequality in a triangle associated with Golden ratio

How to prove this high-degree inequality

Wanted: Positivity certificate for the AM-GM inequality in low dimension

On the inequality $\sum_{i=1}^nx_i^4\sum_{i=1}^nx_i^2 -\sum_{i=1}^nx_i^6 \leq c\left(\sum_{i=1}^nx_i^3\right)^2$

Inequality involving product-of-minus vs minus-of-product for positive integers

Elementary inhomogeneous inequality for three non-negative reals

How to prove that $a + b + 4 \sqrt{1 + a^{2} + b^{2}} \leq 4 \sqrt{a^{2} + b^{2}} + \sqrt{1+b^{2}} + \sqrt{1+a^{2}} + 2 $ for all $a, b > 0$?

Given a polynomial constraint equation in $n$ variables, can one conclude that the sum of the variables is non-negative?