OPTIMAL BOUNDS FOR NEUMAN-SANDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF LOGARITHMIC AND QUADRATIC OR CONTRA-HARMONIC MEANS

被引：61

作者：

Chu, Yuming ^{[1
]}

Zhao, Tiehong ^{[2
]}

Liu, Baoyu ^{[3
]}

机构：

[1] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China

[2] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China

[3] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China

来源：

JOURNAL OF MATHEMATICAL INEQUALITIES | 2014年 / 8卷 / 02期

关键词：

Neuman-Sandor mean; logarithmic mean; quadratic mean; contra-harmonic mean;

D O I：

10.7153/jmi-08-13

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we present the least values alpha(1), alpha(2), and the greatest values beta(1), beta(2) such that the double inequalities alpha L-1(a,b) + 1 (1 - alpha(1))Q(a,b) < M(a,b) < beta L-1(a,b) + (1 - beta(1))Q(a,b) alpha L-2(a,b) + (1 - alpha(2))C(a,b) < M(a,b) < beta L-2(a,b) + (1 - beta(2))C(a,b) hold for all a, b > 0 with a not equal b, where L(a,b), M(a,b), Q(a,b) and C(a,b) are respectively the logarithmic, Neuman-Sandor, quadratic and contra-harmonic means of a and b.

引用

页码：201 / 217

页数：17

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