数学物理学报（英文版）
數學物理學報（英文版）
수학물이학보（영문판）
ACTA MATHEMATICA SCIENTIA
2014年
3期
797-806
,共10页
褚玉明%赵铁洪%宋迎清?
褚玉明%趙鐵洪%宋迎清?
저옥명%조철홍%송영청?
Neuman-S′andor mean%quadratic mean%first Seiffert mean
In this article, we prove that the double inequality P(a, b) + (1 - )Q(a, b) < M(a, b) < P(a, b) + (1 - )Q(a, b) holds for any a, b > 0 with a 6= b if and only if ≥ 1/2 and ≤ [(√ 2 log(1 +√ 2) - 1)]/[(√ 2-2) log(1+√ 2)] = 0.3595 · · · , where M(a, b), Q(a, b), and P(a, b) are the Neuman- S′andor, quadratic, and first Seiffert means of a and b, respectively.
