期刊论文

Chu, Yuming

英文

数学物理学报(英文版)

0252-9602

2014

34

3

797-806

10.1016/S0252-9602(14)60050-3

∗Received March 23, 2013; revised August 29, 2013. This research was supported by the Natural Science Foundation of China under Grants 61374086 and 11371125, and the Natural Science Foundation of Zhejiang Province under Grant LY13A010004.

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In this article, we prove that the double inequality αP(a,b)+1(1-α)Q(a,b) < M(a,b) < βP(a,b)+(1-β)Q(a,b) holds for any a,b > 0 with a ≠ b if and only if α ≥ 1/2 and β ≤ [π(2log(1+2)-1)]/[(2π-2)log(1+2)]=03595. . ., where M(a,b), Q(a,b), and P(a,b) are the Neuman-Sándor, quadratic, and first Seiffert means of a and b, respectively. © 2014 Wuhan ...