Best Possible Inequalities between Generalized Logarithmic Mean and Classical Means

被引：25

作者：

Chu, Yu-Ming ^{[1
]}

Long, Bo-Yong ^{[2
]}

机构：

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

[2] Anhui Univ, Coll Math Sci, Hefei 230039, Peoples R China

来源：

ABSTRACT AND APPLIED ANALYSIS | 2010年

关键词：

MONOTONICITY; RATIO;

D O I：

10.1155/2010/303286

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We answer the question: for alpha, beta,gamma is an element of (0, 1) with alpha + beta + gamma = 1, what are the greatest value p and the least value q, such that the double inequality L-p(a, b) < A(alpha)(a, b)G(beta)(a, b)H-gamma(a, b) < L-q(a, b) holds for all a, b > 0 with a not equal b? Here L-p(a, b), A(a, b), G(a, b), and H(a, b) denote the generalized logarithmic, arithmetic, geometric, and harmonic means of two positive numbers a and b, respectively.

引用

页数：13

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