科研之友
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摘要
We find the greatest value p and the least value q in (0, 1/2) such that the double inequality H (pa + (1 - p)b, pb + (1 - p)a) < I (a, b) < H (qa + (1 - q)b, qb + (1 - q)a) holds for all a, b > 0 with a not equal b. Here, H(a, b), and I(a, b) denote the harmonic and identric means of two positive numbers a and b, respectively.
