Best Possible Bounds for Neuman-Sandor Mean by the Identric, Quadratic and Contraharmonic Means

被引：53
|
作者：
Zhao, Tie-Hong [1 ]
Chu, Yu-Ming [2 ]
Jiang, Yun-Liang [3 ]
Li, Yong-Min [4 ]
机构：
[1] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China
[2] Hunan City Univ, Sch Math & Computat Sci, Yiyang 413000, Peoples R China
[3] Huzhou Teachers Coll, Sch Informat & Engn, Huzhou 313000, Peoples R China
[4] Southeast Univ, Sch Automat, Nanjing 210096, Jiangsu, Peoples R China
来源：
ABSTRACT AND APPLIED ANALYSIS | 2013年
关键词：
INEQUALITIES;
D O I：
10.1155/2013/348326
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that the double inequalities I-alpha 1(a,b)Q(1-alpha 1)(a,b) < M(a,b) < I-beta 1(a,b)Q(1-beta 1)(a,b), I-alpha 2(a,b)C1-alpha 2(a,b) < M(a,b) < I-beta 2(a,b)C1-beta 2(a,b) hold for all a,b > 0 with a not equal b if and only if alpha(1) >= 1/2, beta(1) <= log[root 2log(1 + root 2)]/(1 - log root 2), alpha(2) >= 5/7, and beta(2) <= log[2 log(1 + root 2)], where I(a,b), M(a,b), Q(a,b), and C(a,b) are the identric, Neuman-Sandor, quadratic, and contraharmonic means of a and b, respectively.
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页数：12
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