Optimal one-parameter mean bounds for the convex combination of arithmetic and geometric means

被引：6

作者：

Xia, Weifeng ^{[1
]}

Hou, Shouwei ^{[2
]}

Wang, Gendi ^{[3
]}

Chu, Yuming ^{[3
]}

机构：

[1] Huzhou Teachers Coll, Sch Teacher Educ, Huzhou 313000, Peoples R China

[2] Hangzhou Normal Univ, Sch Sci, Hangzhou 310012, Zhejiang, Peoples R China

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

来源：

JOURNAL OF APPLIED ANALYSIS | 2012年 / 18卷 / 02期

基金：

中国国家自然科学基金;

关键词：

One-parameter mean; arithmetic mean; geometric mean;

D O I：

10.1515/jaa-2012-0013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we answer the question: What are the greatest value p = p (alpha) and least value q = q (alpha) such that the double inequality J(p)(a , b) < alpha A(a , b) + (1 - alpha)G(a , b) < J(q)(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) = a+b/2, G (a ,b) = root ab and J(P)(a ,b) denote the arithmetic, geometric and p-th one-parameter means of a and b, respectively.

引用

页码：197 / 207

页数：11

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