Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables


Authors

Yuanzhe Zhou - The School of Physics and Technology at Wuhan University, China. Vasile Cirtoaje - Department of Automatic Control and Computers, University of Ploiesti, Ploiesti, Romania.


Abstract

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.


Share and Cite

  • Share on Facebook
  • Share on Twitter
  • Share on LinkedIn
ISRP Style

Yuanzhe Zhou, Vasile Cirtoaje, Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables, Journal of Nonlinear Sciences and Applications, 6 (2013), no. 2, 74--85

AMA Style

Zhou Yuanzhe, Cirtoaje Vasile, Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables. J. Nonlinear Sci. Appl. (2013); 6(2):74--85

Chicago/Turabian Style

Zhou, Yuanzhe, Cirtoaje, Vasile. "Some strong sufficient conditions for cyclic homogeneous polynomial inequalities of degree four in nonnegative variables." Journal of Nonlinear Sciences and Applications, 6, no. 2 (2013): 74--85


Keywords


MSC


References