Optimal bounds for Neuman-Sandor mean in terms of the convex combination of the logarithmic and the second Seiffert means

被引：2
|
作者：
Chen, Jing-Jing [1 ]
Lei, Jian-Jun [1 ]
Long, Bo-Yong [1 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230601, Anhui, Peoples R China
来源：
JOURNAL OF INEQUALITIES AND APPLICATIONS | 2017年
关键词：
Neuman-Sandor mean; logarithmic mean; the second Seiffert mean; SHARP BOUNDS; INEQUALITIES; 1ST;
D O I：
10.1186/s13660-017-1516-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In the article, we prove that the double inequality alpha L(a, b) + (1 - alpha) T(a, b) < NS(a, b) < beta L(a, b) + (1 - beta) T(a, b) holds for a, b > 0 with a not equal b if and only if alpha = 1/4 and beta <= 1 - pi/[4 log(1 +root 2)], where NS(a, b), L(a, b) and T(a, b) denote the Neuman-Sandor, logarithmic and second Seiffert means of two positive numbers a and b, respectively.
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页数：11
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