Geodesic
Necessary and sucient conditions for symmetric homogeneous polynomial inequalities of degree four and six in real variables
Cirtoaje, Vasile1
1 Department of Automatic Control and Computers, University of Ploiesti, Ploiesti, Romania
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 5, p. 307-320.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Let $f_n(x; y; z)$ be a symmetric homogeneous polynomial of degree $n = 4$ or $n = 6$, in three real variables. We give necessary and sufficient conditions to have $f_n(x; y; z) \geq 0$ for all real numbers $x; y; z$. Then, we apply the obtained results to prove several relevant symmetric homogeneous polynomial inequalities of degree four and six.
DOI : 10.22436/jnsa.005.05.01
Classification : 26B25
Keywords: Symmetric homogeneous polynomial, necessary and sufficient conditions, real variables.

Cirtoaje, Vasile 1

1 Department of Automatic Control and Computers, University of Ploiesti, Ploiesti, Romania 
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Cirtoaje, Vasile. Necessary and sucient conditions for symmetric homogeneous polynomial inequalities of degree four and six in real variables. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 5, p. 307-320. doi : 10.22436/jnsa.005.05.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.05.01/

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