On the Cyclic Homogeneous Polynomial Inequalities of Degree Four

@inproceedings{ONTROL2009OnTC,
  title={On the Cyclic Homogeneous Polynomial Inequalities of Degree Four},
  author={VASILE CIRTOAJE D EPARTMENT OF A UTOMATIC C ONTROL and C OMPUTERS U NIVERSITY OF P LOIESTI R OMANIA},
  year={2009}
}
  • VASILE CIRTOAJE D EPARTMENT OF A UTOMATIC C ONTROL, C OMPUTERS U NIVERSITY OF P LOIESTI R OMANIA
  • Published 2009
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 havef(x, y, z) ≥ 0 for any real numbersx, y, z. We also give the necessary and sufficient conditions to havef(x, y, z) ≥ 0 for the case whenf is symmetric andx, y, z are nonnegative real numbers. Finally, some new inequalities with cyclic homogeneous polynomials of degree four are presented.