一类齐次对称多项式上的切比雪夫不等式

本文借助于控制不等式及数学归纳法，将著名的切比雪夫不等式推广到m次一般齐次对称多项式上(如文中定理及引理7)，并将此结果用于对称平均等．旨在展示证明解析不等式的一些有效的方法和技巧，同时为数学研究特别是高维几何研究提供一些新的有趣而有用的解析不等式．

CHEBYSHEV''''S INEQUALITY FOR A CLASS OF HOMOGENEOUS AND SYMMETRIC POLYNOMIALS

By means of majorized inequalities and mathematical induction, the well known Chebyshev's inequality is generalized to homogeneous and symmetric polynomials of degree m (e.g., Theorem and Lemma 7 of this paper). As an application, some inequalities involving symmetric mean and others are obtained. Our main purposes are to display some methods and techniques as well as to establish several new, useful and interesting analytic inequalities for mathematicl study (especially, for higher dimensional geometry).