An Optimal Double Inequality between Seiffert and Geometric Means
[摘要] Forα,β∈(0,1/2)we prove that the double inequalityG(αa+(1−α)b,αb+(1−α)a)0witha≠bif and only ifα≤(1−1−4/π2)/2andβ≥(3−3)/6. Here,G(a,b)andP(a,b)denote the geometric and Seiffert means of two positive numbersaandb, respectively.
