Sharp Power Mean Bounds for the One-Parameter Harmonic Mean
We present the best possible parameters α=α(r) and β=β(r) such that the double inequality Mα(a,b)<Hr(a,b)<Mβ(a,b) holds for all r∈(0, 1/2) and a, b>0 with a≠b, where Mp(a, b)=[(ap+bp)/2]1/p (p≠0) and M0(a, b)=ab and Hr(a, b)=2[ra+(1-r)b][rb+(1-r)a]/(a+b) are the power and one-parameter har...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/517647 |
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