SHARP BOUNDS FOR NEUMAN-SANDOR MEAN IN TERMS OF THE CONVEX COMBINATION OF QUADRATIC AND FIRST SEIFFERT MEANS

被引：50
|
作者：
Chu, Yuming [1 ]
Zhao, Tiehong [2 ]
Song, Yingqing [1 ]
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
来源：
ACTA MATHEMATICA SCIENTIA | 2014年 / 34卷 / 03期
关键词：
Neuman-Sandor mean; quadratic mean; first Seiffert mean; INEQUALITIES;
D O I：
10.1016/S0252-9602(14)60050-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we prove that the double inequality alpha P(a, b) + (1-alpha)Q(a, b) < M (a,b) < beta P(a, b) + (1-beta)Q (a,b) holds for any a, b > 0 with a not equal b if and only if alpha > 1/2 and beta <= [pi root 2(log(1 + root 2 -1)] /[root 2 pi-2) log(1 + root 2)] = 0.359..., where M(a, b), Q(a, b), and P(a, b) are the Neuman-Sandor, quadratic, and first Seiffert means of a and b, respectively.
引用
收藏
页码：797 / 806
页数：10
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