A Sharp Double Inequality between Seiffert, Arithmetic, and Geometric Means
For fixed s≥1 and any t1,t2∈(0,1/2) we prove that the double inequality Gs(t1a+(1-t1)b,t1b+(1-t1)a)A1-s(a,b)<P(a,b)<Gs(t2a+(1-t2)b,t2b+(1-t2)a)A1-s(a,b) holds for all a,b>0 with a≠b if and only if t1≤(1-1-(2/π)2/s)/2 and t2≥(1-1/3s)/2. Here, P(a,b), A(a,b) and G(a,b) denote the Seiffert, ar...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/684834 |