OPTIMAL CONVEX COMBINATION BOUNDS OF SEIFFERT AND GEOMETRIC MEANS FOR THE ARITHMETIC MEAN

被引：30
|
作者：
Chu, Yu-Ming [1 ]
Zong, Cheng [2 ]
Wang, Gen-Di [1 ]
机构：
[1] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China
[2] Hangzhou Normal Univ, Sch Sci, Hangzhou 310012, Zhejiang, Peoples R China
来源：
JOURNAL OF MATHEMATICAL INEQUALITIES | 2011年 / 5卷 / 03期
关键词：
Seiffert mean; geometric mean; arithmetic mean;
D O I：
10.7153/jmi-05-37
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We find the greatest value alpha and the least value beta such that the double inequality alpha T(a,b) + (1 - alpha)G(a,b) < A(a,b) < beta T(a,b) + (1 - beta) G(a,b) holds for all a,b > 0 with a not equal b. Here T(a,b), G(a,b), and A(a,b) denote the Seiffert, geometric, and arithmetic means of two positive numbers a and b, respectively.
引用
收藏
页码：429 / 434
页数：6
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