OPTIMAL ONE-PARAMETER MEAN BOUNDS FOR THE CONVEX COMBINATION OF ARITHMETIC AND LOGARITHMIC MEANS

被引：2
|
作者：
He, Zai-Yin [1 ]
Wang, Miao-Kun [1 ]
Chu, Yu-Ming [1 ]
机构：
[1] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China
来源：
JOURNAL OF MATHEMATICAL INEQUALITIES | 2015年 / 9卷 / 03期
关键词：
One-parameter mean; arithmetic mean; logarithmic mean; INEQUALITIES; VARIABLES;
D O I：
10.7153/jmi-09-58
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We find the greatest value p(1) = p(1)(alpha) and the least value p(2) = p(2)(alpha) such that the double inequality J(p1) (a, b) < alpha A(a, b)+(1-alpha)L(a, b) < J(p2) (a, b) holds for any alpha is an element of (0,1) and all a, b > 0 with a not equal b. Here, A(a, b), L(a, b) and J(p)(a, b) denote the arithmetic, logarithmic and p-th one-parameter means of two positive numbers a and b, respectively.
引用
收藏
页码：699 / 707
页数：9
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