A Best Possible Double Inequality for Power Mean
We answer the question: for any p,q∈ℝ with p≠q and p≠-q, what are the greatest value λ=λ(p,q) and the least value μ=μ(p,q), such that the double inequality Mλ(a,b)<Mp(a,b)Mq(a,b)<Mμ(a,b) holds for all a,b>0 with a≠b? Where Mp(a,b) is the pth power mean of two positive numbers a and b....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/379785 |
| Summary: | We answer the question: for any p,q∈ℝ with p≠q and p≠-q, what are the greatest value λ=λ(p,q) and the least value μ=μ(p,q), such that the double inequality Mλ(a,b)<Mp(a,b)Mq(a,b)<Mμ(a,b) holds for all a,b>0 with a≠b? Where Mp(a,b) is the pth power mean of two positive numbers a and b. |
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| ISSN: | 1110-757X 1687-0042 |