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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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