一类对称函数的Schur—几何凸性及Schur—调和凸性

摘要

The Schur-convex functions have 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,we disscus Schur convexity and Schur multiplicatively convexity and Schur harmonic convexity for a class of symmetric functions.%Schur—凸函数在分析不等式、广义平均值、统计实验、图和矩阵、组合优化、可靠性、信息安全、随机排序和其它相关领域均有重要作用,故研究n元对称函数的Schur—凸性具有重要意义.在本文中,讨论了一类对称函数的Schur—凸性、Schur—几何凸性及Schur—调和凸性.