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.
引用
收藏
页码：191 / 197
页数：7
相关论文
共 50 条
  • [1] On one-parameter family of bivariate means
    Edward Neuman
    [J]. Aequationes mathematicae, 2012, 83 : 191 - 197
  • [2] A ONE-PARAMETER FAMILY OF BIVARIATE MEANS
    Neuman, Edward
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2013, 7 (03): : 399 - 412
  • [3] Sharp bounds for Neuman means in terms of one-parameter family of bivariate means
    Zhi-Hua Shao
    Wei-Mao Qian
    Yu-Ming Chu
    [J]. Journal of Inequalities and Applications, 2014
  • [4] Sharp bounds for Neuman means in terms of one-parameter family of bivariate means
    Shao, Zhi-Hua
    Qian, Wei-Mao
    Chu, Yu-Ming
    [J]. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
  • [5] SHARP BOUNDS FOR SANDOR-YANG MEANS IN TERMS OF ONE-PARAMETER FAMILY OF BIVARIATE MEANS
    Yang, Yue-Ying
    Qian, Wei-Mao
    Xu, Hui-Zuo
    [J]. JOURNAL OF MATHEMATICAL INEQUALITIES, 2019, 13 (04): : 1181 - 1196
  • [6] PROPERTIES OF A ONE-PARAMETER FAMILY OF BIVARIATE DISTRIBUTIONS WITH SPECIFIED MARGINALS
    NELSEN, RB
    [J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 1986, 15 (11) : 3277 - 3285
  • [7] ONE-PARAMETER FAMILIES OF BIVARIATE DISTRIBUTIONS WITH FIXED MARGINALS
    KIMELDORF, G
    SAMPSON, A
    [J]. COMMUNICATIONS IN STATISTICS, 1975, 4 (03): : 293 - 301
  • [8] Hirzebruch surfaces in a one-parameter family
    Battaglia, Fiammetta
    Prato, Elisa
    Zaffran, Dan
    [J]. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2019, 12 (1-2): : 293 - 305
  • [9] ONE-PARAMETER FAMILY OF SEQUENCE TRANSFORMATIONS
    VANDENBROECK, JM
    SCHWARTZ, LW
    [J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1979, 10 (03) : 658 - 666
  • [10] ONE-PARAMETER FAMILY OF AFFINE PLANES
    KAMBAYASHI, T
    [J]. INVENTIONES MATHEMATICAE, 1979, 52 (03) : 275 - 281
12345