%0 Journal Article
%T Some Strong Sufficient Conditions for Cyclic Homogeneous Polynomial Inequalities of Degree Four in Real Variables
%A Vasile Cirtoaje
%A Yuanzhe Zhou
%J Journal of Nonlinear Analysis and Application
%D 2012
%I International Scientific Publications and Consulting Services (ISPACS)
%R 10.5899/2012/jnaa-00151
%X We establish some strong sufficient conditions such that the inequality $f_4(x,y,z)ge 0$ holds for any real numbers $x,y,z,$ where $f_4(x,y,z)$ is a cyclic homogeneous polynomial of degree four. In addition, we give a conjecture which states some new necessary and sufficient conditions such that the inequality $f_4(x,y,z)ge 0$ holds for any real numbers $x,y,z.$ Several applications are given to show the effectiveness of the proposed method.
%K Cyclic homogeneous inequality
%K fourth degree polynomial
%K three real variables
%K strong sufficient conditions
%K necessary conditions
%U http://www.ispacs.com/journals/jnaa/2012/jnaa-00151/article.pdf