A Strong Method for Symmetric Homogeneous Polynomial Inequalities of Degree Six in Nonnegative Real Variables

摘要

Let f ₆ (x, y, z) be a symmetric homogeneous polynomial of degree six. Based on cancelling the high coefficient of f ₆ (x, y, z) , we give some practical sufficient conditions to have f ₆ (x, y, z) ≥ 0 for any nonnegative real variables x, y, z . Some applications are given in order to emphasize the effectiveness of the proposed method.