Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means
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.
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/520648 |