摘要
For p ∈ R, the generalized logarithmic mean Lp(a, b) and Seiffert's mean T(a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality Lp(a, b) 〈 T(a,b) 〈 Lq(a,b) holds for all a,b 〉 0 and a ≠ b.
For p ∈ R, the generalized logarithmic mean Lp(a, b) and Seiffert's mean T(a, b) of two positive real numbers a and b are defined in (1.1) and (1.2) below respectively. In this paper, we find the greatest p and least q such that the double-inequality Lp(a, b) 〈 T(a,b) 〈 Lq(a,b) holds for all a,b 〉 0 and a ≠ b.
基金
supported by the National Natural Science Foundation of China (11071069 and 11171307)
Natural Science Foundation of Hunan Province(09JJ6003)
Innovation Team Foundation of the Department of Education of Zhejiang Province (T200924)