数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1619-1626.doi: 10.1016/S0252-9602(12)60128-3

• 论文 • 上一篇    下一篇

THE OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR SEIFFERT'S MEAN

褚玉明1|王淼坤2|王根娣3   

  1. 1.Department of Mathematics, Hunan City University, Yiyang 413000, China|2.College of Mathematics and Econometrics, Hunan University, Changsha 410082, China|3.Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
  • 收稿日期:2010-01-12 修回日期:2011-08-25 出版日期:2012-07-20 发布日期:2012-07-20
  • 基金资助:

    This research was supported by the National Natural Science Foundation of China (11071069 and 11171307), Natural Science Foundation of Hunan Province (09JJ6003) and Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924).

THE OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR SEIFFERT'S MEAN

 CHU Yu-Ming1, WANG Miao-Kun2, WANG Gen-Di3   

  1. 1.Department of Mathematics, Hunan City University, Yiyang 413000, China|2.College of Mathematics and Econometrics, Hunan University, Changsha 410082, China|3.Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China
  • Received:2010-01-12 Revised:2011-08-25 Online:2012-07-20 Published:2012-07-20
  • Supported by:

    This research was supported by the National Natural Science Foundation of China (11071069 and 11171307), Natural Science Foundation of Hunan Province (09JJ6003) and Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924).

摘要:

For p R, the generalized logarithmic mean Lp(a, b) and Seiffert's mean T(a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality Lp(a, b) <T(a, b) < Lq(a, b) holds for all a, b > 0 and a ≠ b.

关键词: generalized logarithmic mean, Seifferts mean, power mean

Abstract:

For p R, the generalized logarithmic mean Lp(a, b) and Seiffert's mean T(a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality Lp(a, b) <T(a, b) < Lq(a, b) holds for all a, b > 0 and a ≠ b.

Key words: generalized logarithmic mean, Seifferts mean, power mean

中图分类号: 

  • 26E60