数学物理学报 ›› 2013, Vol. 33 ›› Issue (2): 298-308.

• 论文 • 上一篇    下一篇

广义对数平均, 算术平均和几何平均之间的不等式

褚玉明|王淼坤   

  1. 湖南城市学院数学与计算科学学院 湖南益阳 413000;湖南大学数学与计量经济学院 长沙 410082
  • 收稿日期:2011-02-23 修回日期:2012-11-23 出版日期:2013-04-25 发布日期:2013-04-25
  • 基金资助:

    国家自然科学基金 (11071059, 11071069, 11171307) 资助

Inequalities Between Generalized Logarithmic, Arithmetic and Geometric Means

 CHU Yu-Ming, WANG Miao-Kun   

  1. College of Mathematics and Computing Science, Hunan City University, Hunan Yiyang 413000;College of Mathematics and Econometrics, Hunan University, Changsha 410082
  • Received:2011-02-23 Revised:2012-11-23 Online:2013-04-25 Published:2013-04-25
  • Supported by:

    国家自然科学基金 (11071059, 11071069, 11171307) 资助

摘要:

给出了算术平均和几何平均组合的最佳广义对数平均上下界. 所获结果解决了文献[21], Long B Y, Chu Y M. Optimal inequalities for generalized logarithmic, arithmetic, and geometric means. J Inequal Appl, 2010, Art ID 806825]中所提出的两个公开问题.

关键词: 广义对数平均, 算术平均, 几何平均

Abstract:

In this paper, we establish the best lower and upper bounds for combination of the arithmetic and geometric means by the generalized logarithmic mean. These results solve two open problems posed in the paper [21].

Key words: Generalized logarithmic mean, Arithmetic mean,  Geometric mean

中图分类号: 

  • 26E60