Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means
oleh: Yu-Ming Chu, Shan-Shan Wang, Cheng Zong
| Format: | Article |
|---|---|
| Diterbitkan: | Wiley 2011-01-01 |
Deskripsi
We find the least value λ∈(0,1) and the greatest value p=p(α) such that αH(a,b)+(1−α)L(a,b)>Mp(a,b) for α∈[λ,1) and all a,b>0 with a≠b, where H(a,b), L(a,b), and Mp(a,b) are the harmonic, logarithmic, and p-th power means of two positive numbers a and b, respectively.