一类对称函数的Schur调和凸及其应用（英文）  

SCHUR HARMONIC CONVEXITY FOR A CLASS OF SYMMETRIC FUNCTIONS WITH APPLICATIONS

作　　者：王文[1] 杨世国[1] 

机构地区：[1]合肥师范学院数学系,合肥230601

出　　处：《南京大学学报（数学半年刊）》2015年第2期129-143,共15页Journal of Nanjing University(Mathematical Biquarterly)

基　　金：Supported by the Doctoral Programs Foundation of Education Ministry of China(20113401110009);Natural Science Research Project of Hefei Normal University(2012kj11);Universities Natural Science Foundation of Anhui Province(KJ2013A220)

摘　　要：本文主要证明了对称函数∑rn(f(x))=∑1≤■〈■〈...〈■〈n f(■rj=1x_(ij)^(1/r))和∑rn(f^(-1)(x))是Schur调和凸的,其中x∈R_+~n且r∈N^+={1,2,…,n}.利用建立的结果证明了一些对称函数是Schur调和凸的.最后利用优化理论和文中建立的主要结果给出了一些分析不等式和几何不等式.The main purpose of the paper is to prove that r∑n（f（x））=1≤i1≤i2〈…〈ir≤n∑f（rПj=1x1rij） and r∑n（f-1（x））are Schur harmonic convex for x∈Rn＋ and r∈N＋={1,2,…,n）.Asits application, we prove that several symmetric functions are Schur harmonic convex. By using the theory of majorization, several inequalities are established to show the applications.

关 键 词：Schur调和凸 对称函数 不等式 单形 

分 类 号：O174.13[理学—数学] O184[理学—基础数学]