SOME PROPERTIES FOR A CLASS OF SYMMETRIC FUNCTIONS WITH APPLICATIONS

被引：10

作者：

Xia, Wei-Feng ^{[1
]}

Zhang, Xiao-Hui ^{[2
]}

Wang, Gen-Di ^{[2
]}

Chu, Yu-Ming ^{[1
]}

机构：

[1] Huzhou Teachers Coll, Sch Teachers Educ, Huzhou 313000, Peoples R China

[2] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China

来源：

INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS | 2012年 / 43卷 / 03期

关键词：

Symmetric function; Schur convex; Schur multiplicatively convex; Schur harmonic convex; SCHUR-HARMONIC-CONVEXITY; DUAL FORM; INEQUALITIES; CONCAVITY; RESPECT;

D O I：

10.1007/s13226-012-0012-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For x = (x(1), x(2), ... , x(n)) is an element of R-+(n), the symmetric function psi(n)(x, r) is defined by psi(n)(x, r) = psi(n)(x(1), x(2), ... , x(n);r) = Sigma(1 <= i1<i2...<ir <= n) Pi(r)(j=1) 1 + x(ij)/x(ij), where r = 1, 2, ... , n and i(1), i(2), ... , i(n) are integers. In this article, the Schur convexity, Schur multiplicative convexity and Schur harmonic convexity of psi(n)(x, r) are discussed. As applications, some inequalities are established by use of the theory of majorization.

引用

页码：227 / 249

页数：23

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