Optimal Lehmer Mean Bounds for the Toader Mean

被引：111

作者：

Chu, Yu-Ming ^{[1
]}

Wang, Miao-Kun ^{[1
]}

机构：

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

来源：

RESULTS IN MATHEMATICS | 2012年 / 61卷 / 3-4期

基金：

中国国家自然科学基金;

关键词：

Lehmer mean; Toader mean; power mean; INEQUALITIES; HOLDER;

D O I：

10.1007/s00025-010-0090-9

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 such that the double inequality L (p) (a, b) < T(a, b) < L (q) (a, b) holds for all a, b > 0 with a not equal b, and give a new upper bound for the complete elliptic integral of the second kind. Here and L (p) (a, b) = (a (p+1) + b (p+1))/(a (p) + b (p) ) denote the Toader and p-th Lehmer means of two positive numbers a and b, respectively.

引用

页码：223 / 229

页数：7

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