Sharp Power Mean Bounds for the Combination of Seiffert and Geometric Means
oleh: Yu-Ming Chu, Ye-Fang Qiu, Miao-Kun Wang
| Format: | Article |
|---|---|
| Diterbitkan: | Wiley 2010-01-01 |
Deskripsi
We answer the question: for α∈(0,1), what are the greatest value p and the least value q such that the double inequality Mp(a,b)<Pα(a,b)G1−α(a,b)<Mq(a,b) holds for all a,b>0 with a≠b. Here, Mp(a,b), P(a,b), and G(a,b) denote the power of order p, Seiffert, and geometric means of two positive numbers a and b, respectively.