关于一类对称函数的Schur凸性研究

Schur Convexity of a Class of Symmetric Functions

Schur凸函数在分析不等式、广义均值、实验统计、图表和矩阵、组合优化、可靠性、信息安全、随机排序等领域有着重要的应用.所以,研究多个变量的对称函数的Schur凸性有着重要的意义.本文推广了关开中的对称函数,得到了一类新的对称函数,并利用著名的Schur条件,研究了这类对称函数的Schur凸性.

The Schur-convex function has many important applications in analytic inequalities,generalized means,statistics experiment,chart and matrix,combinatorial optimization,reliability,information security,random sorting,etc.So it is important that Schur-convexity for symmetric functions of several variables is researched.In this paper,Guan’s symmetric function was improved,and a class of symmetric functions were derived.By so-called Schur’s condition,Schur-convexity is studied for a class of symmetric functions.