An Optimal Double Inequality between Seiffert and Geometric Means
For α,β∈(0,1/2) we prove that the double inequality G(αa+(1−α)b,αb+(1−α)a)<P(a,b)<G(βa+(1−β)b,βb+(1−β)a) holds for all a,b>0 with a≠b if and only if α≤(1−1−4/π2)/2 and β≥(3−3)/6. Here, G(a,b) and P(a,b) denote the geometric and Seiffert 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: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/261237 |