On one-parameter family of bivariate means

被引：11
|
作者：
Neuman, Edward [1 ]
机构：
[1] So Illinois Univ, Dept Math, Carbondale, IL 62901 USA
来源：
AEQUATIONES MATHEMATICAE | 2012年 / 83卷 / 1-2期
关键词：
Bivariate means; Schwab-Borchardt mean; inverse Jacobian elliptic functions; completely symmetric elliptic integral; inequalities;
D O I：
10.1007/s00010-011-0099-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A one-parameter family of bivariate means is introduced. They are defined in terms of the inverse functions of Jacobian elliptic functions cn and nc. It is shown that the new means are symmetric and homogeneous of degree one in their variables. Members of this family of means interpolate an inequality which connects two Schwab-Borchardt means. Computable lower and upper bounds for the new mean are also established.
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页码：191 / 197
页数：7
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