Journal of Advances in Mathematics and Computer Science

Quartic Cyclic Homogeneous Polynomial Inequalities of Three Nonnegative Variables

Yuanzhe Zhou *

Department of Physics, University Claude Bernard Lyon 1, France.

*Author to whom correspondence should be addressed.

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Abstract

We present and prove a set of necessary and sufficient conditions that the inequality f₄(x, y, z) ≥ 0 holds for all nonnegative real variables x, y, z, where f₄(x, y, z) is a cyclic homogeneous polynomial of degree four which satisfies f₄(1, 1, 1) = 0.

Keywords: Cyclic homogeneous inequality, quartic polynomial, nonnegative variables, necessary and sufficient conditions

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