%0 Journal Article
%T The Schur Convexity and Inequalities for a Class of Symmetric Functions<br>类对称函数的Schur凸性和不等式
%A LONG Bo-Yong
%A CHU Yu-Ming
%A <br>龙波涌
%A 褚玉明
%J 数学物理学报(A辑)
%D 2012
%I 
%X For x = (x1, x2,···, xn) ∈ (0,1) and r ∈ {1, 2,···, n}, the symmetric function Fn(x, r) is defined by Fn(x, r) = Fn(x1, x2,···, xn; r) =∏1≤i1<i2<···<ir≤n ∑ j=1r(1+xi3/1- xi3)1/r, where i1, i2, ···, ir are integers. In this paper, it is proved that Fn(x,r) is Schur convex, Schur multiplicatively convex and Schur harmonic convex on (0,1)n. As applications, some inequalities are established by use of the theory of majorization.
%K Schur convexzz
%K Schur multiplicatively convexzz
%K Schur harmonic convexzz<br>Schur凸
%K Schur乘性凸
%K Schur调和凸
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=46DBF3E8FC2736F0530DEAED635D590F&yid=99E9153A83D4CB11&vid=9971A5E270697F23&iid=CA4FD0336C81A37A&sid=E203FB1A272C9DD2&eid=CFAC5CB624A41AFD&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=0