An optimal double inequality between geometric and identric means

被引：27

作者：

Wang, Miao-Kun ^{[1
]}

Wang, Zi-Kui ^{[2
]}

Chu, Yu-Ming ^{[1
]}

机构：

[1] Huzhou Teachers Coll, Dept Math, Huzhou 313000, Peoples R China

[2] Hangzhou Normal Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2012年 / 25卷 / 03期

关键词：

Geometric mean; Identric mean; Inequality; SHARP INEQUALITIES; 2; VARIABLES;

D O I：

10.1016/j.aml.2011.09.038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We find the greatest value p and least value q in (0, 1/2) such that the double inequality G(pa + (1 - p)b, pb + (1 - p)a) < I(a, b) < G(qa + (1 - q)b, qb + (1 - q)a) holds for all a, b > 0 with a not equal b. Here, G(a, b), and 1(a, b) denote the geometric, and identric means of two positive numbers a and b, respectively. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：471 / 475

页数：5

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