The optimal generalized logarithmic mean bounds for Seiffert's mean

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.