关于几个平均数商的Schur—凸性的研究  

Schur- Convexity for Quotient of Some Means

作　　者：尹红萍[1] 包金山[1] 吴英[1] 

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028043

出　　处：《内蒙古民族大学学报（自然科学版）》2011年第6期637-641,共5页Journal of Inner Mongolia Minzu University：Natural Sciences

摘　　要：多元函数的Schur—凸性理论是重要的研究课题,国内外众多学者讨论多元函数的Schur—凸性问题.本文对某些著名平均值(如算术平均,几何平均,调和平均,根平方平均等)的商进行了讨论,并研究了其在R+2上的Schur—凸性、Schur—几何凸性以及Schur—调和凸性问题,得到了几个一般结果.The theories of the Schur-concavity of Multivariate Function is an significant subject, lots of scholars are studying the question at home and abroad. In this article,we discussed the difference of some famous means such as arithmetic mean, geometric mean, harmonic mean, root-square mean,etc. And the Schur- concavity, Schur- geometry concavity and Schur- harmonic concavity in for some inequalities related to the difference of means are obtained.

关 键 词：算术平均 Schur—几何凸性 Schur—调和凸性 根平方平均 平方根平均 HERON平均 商 

分 类 号：O151.25[理学—数学]