Geodesic
Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables
Zhou, Yuanzhe1 ; Cirtoaje, Vasile2
1 The School of Physics and Technology at Wuhan University, China
2 Department of Automatic Control and Computers, University of Ploiesti, Ploiesti, Romania
Journal of nonlinear sciences and its applications, Tome 6 (2013) no. 2, p. 74-85.

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

We establish some strong sufficient conditions that the inequality $f_4(x; y; z) \geq 0$ holds for all nonnegative real numbers $x; y; z$, where$ f_4(x; y; z)$ is a cyclic homogeneous polynomial of degree four. In addition, in the case $f_4(1; 1; 1) = 0$ and also in the case when the inequality $f_4(x; y; z) \geq 0$ does not hold for all real numbers $x; y; z$, we conjecture that the proposed sufficient conditions are also necessary that$ f_4(x; y; z) \geq 0$ for all nonnegative real numbers $x; y; z$. Several applications are given to show the effectiveness of the proposed methods.
DOI : 10.22436/jnsa.006.02.03
Classification : 26D05
Keywords: Cyclic homogeneous polynomial, strong sufficient conditions, necessary and sufficient conditions, nonnegative real variables.

Zhou, Yuanzhe 1 ; Cirtoaje, Vasile 2

1 The School of Physics and Technology at Wuhan University, China
2 Department of Automatic Control and Computers, University of Ploiesti, Ploiesti, Romania 
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Zhou, Yuanzhe; Cirtoaje, Vasile. Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables. Journal of nonlinear sciences and its applications, Tome 6 (2013) no. 2, p. 74-85. doi : 10.22436/jnsa.006.02.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.006.02.03/

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