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  Volume 10, Issue 3, Article 67
 
On the Cyclic Homogeneous Polynomial Inequalities of Degree Four
    Authors: Vasile Cirtoaje,  
    Keywords: Cyclic inequality, Symmetric inequality, Necessity and sufficiency, Homogeneous polynomial of degree four.  
    Date Received: 20/04/2009  
    Date Accepted: 01/07/2009  
    Subject Codes:

26D05.

  
    Editors: Narendra K. Govil,  
 
    Abstract:

Let $ f(x,y,z)$ be a cyclic homogeneous polynomial of degree four with three variables which satisfies $ f(1,1,1)=0$. In this paper, we give the necessary and sufficient conditions to have $ f(x,y,z) ge 0$ for any real numbers $ x,y,z$. We also give the necessary and sufficient conditions to have $ f(x,y,z) ge 0$ for the case when $ f$ is symmetric and $ x,y,z$ are nonnegative real numbers. Finally, some new inequalities with cyclic homogeneous polynomials of degree four are presented.

         
       
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