第一类Seiffert平均和对数平均的广义海伦平均精确界

数学物理学报 ›› 2013, Vol. 33 ›› Issue (3): 568-572.

第一类Seiffert平均和对数平均的广义海伦平均精确界

高红亚|郭建玲|李梦华

河北大学数学与计算机学院河北保定 071002

收稿日期:2011-12-13 修回日期:2013-01-09 出版日期:2013-06-25 发布日期:2013-06-25
基金资助:
国家自然科学基金(10971224)和河北省自然科学基金(A2011201011)资助

Sharp Bounds for the first Seiffert and Logarithmic Means in Terms of Generalized Heronian Mean

GAO Hong-Ya, GUO Jian-Ling, LI Meng-Hua

College of Mathematics and Computer Science, Hebei University, Hebei Baoding 071002

Received:2011-12-13 Revised:2013-01-09 Online:2013-06-25 Published:2013-06-25
Supported by:
国家自然科学基金(10971224)和河北省自然科学基金(A2011201011)资助

摘要/Abstract

摘要：

得到最小值α, γ和最大值β, τ, 使得对所有a, b>0, a≠b, 不等式
H_α(a, b)<P(a, b)<H_β (a, b) ; 和H_γ(a, b)<L(a, b)<H_τ(a, b)
成立. 这里, H_ω(a, b), P(a, b)和L(a, b)分别是两个正数a和b的广义海伦平均, 第一类Seiffert平均和对数平均.

关键词: 精确界, 第一类Seiffert平均, 对数平均, 广义海伦平均

Abstract:

We find the least values α, γ and the greatest values β, τ, such that the inequalities
H_α(a, b)<P(a, b)<H_β (a, b) ; 和H_γ(a, b)<L(a, b)<H_τ(a, b)
hold for all a, b>0 with a≠b. Here, H_ω(a, b), P(a, b), and L(a, b) be the generalized Heronian, the first Seiffert and the
logarithmic means of two positive numbers a and b, respectively.

Key words: Sharp bound, The first Seiffert mean, Logarithmic mean, Generalized Heronian mean

中图分类号:

26D15

高红亚, 郭建玲, 李梦华. 第一类Seiffert平均和对数平均的广义海伦平均精确界[J]. 数学物理学报, 2013, 33(3): 568-572.

GAO Hong-Ya, GUO Jian-Ling, LI Meng-Hua. Sharp Bounds for the first Seiffert and Logarithmic Means in Terms of Generalized Heronian Mean[J]. Acta mathematica scientia,Series A, 2013, 33(3): 568-572.

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