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# 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} }

- 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.