We present the best possible parameters alpha = alpha(r) and beta = beta(r) such that the double inequality M-alpha(a, b) < H-r(a, b) < M-beta (a, b) holds for all r is an element of ( 0, 1/2) and a, b > 0 with a not equal b where M-p (a, b) = [(a(p) + b(p))/2](1/p) (p not equal 0) and M-0 (a, b) = root ab and H-r (a, b) = 2[ra + (1 - r)b][rb + (1 - r)a]/(a +b) are the power and one- parameter harmonic means of a and b, respectively.
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