Abstract
For 1 < r < +∞, we find the least value α and the greatest value β such that the inequality Hα(a, b) < Ar(a, b) < Hβ(a, b) holds for all a, b > 0 with a ≠ b. Here, Hω(a, b) and Ar(a, b) are the generalized Heronian and the power means of two positive numbers a and b, respectively.
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