Optimal Inequalities between Harmonic, Geometric, Logarithmic, and Arithmetic-Geometric Means
We find the least values p, q, and s in (0, 1/2) such that the inequalities H(pa+(1 − p)b, pb+(1 − p)a)>AG(a,b), G(qa+(1−q)b, qb+(1−q)a)>AG(a,b), and L(sa+(1−s)b,sb+(1−s)a)> AG(a,b) hold for all a,b>0 with a≠b, respectively. Here AG(a,b), H(a,b), G(a,b), and L(a,b) denote the arithmetic-...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/618929 |
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