The Schur multiplicative and harmonic convexities of the complete symmetric function

被引：77
作者：
Chu, Y. -M. [1 ]
Wang, G. -D. [1 ]
Zhang, X. -H. [1 ]
机构：
[1] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China
来源：
MATHEMATISCHE NACHRICHTEN | 2011年 / 284卷 / 5-6期
关键词：
Complete symmetric function; Schur multiplicative convexity; Schur harmonic convexity; theory of majorization; EXTENDED MEAN-VALUES; INEQUALITIES; FAMILIES;
D O I：
10.1002/mana.200810197
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper investigates the Schur multiplicative and harmonic convexities of the complete symmetric function F-n(x, r) = Sigma(i1+i2+center dot center dot center dot+in-r)x(1)(i1)x(2)(i2) center dot center dot center dot x(n)(in) and the function phi n (x, r) = F-n(x, r)/F-n (x, r-1), where i(1), i(2), center dot center dot center dot , i(n) are nonnegative integers and r >= 1. As applications, some analytic inequalities are established by use of the theory of majorization. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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页码：653 / 663
页数：11
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