科研之友
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摘要
For k is an element of [0, +infinity), the power-type Heron mean H-k(a,b) and the Seiffert mean T(a,b) of two positive real numbers a and b are defined by H-k(a,b) = ((a(k) + (ab()k/2) + b(k))/3)(1/k), k not equal 0; H-k(a,b) =root ab, k = 0 and T(a,b) = (a - b)/2arctan((a - b)/(a + b)), a not equal b; T(a,b) = a, a = b, respectively. In this paper, we find the greatest value p and the least value q such that the double inequality H-p(a,b) < T(a,b) < H-q(a,b) holds for all a, b > 0 with a not equal b.
