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In this article, we prove that the double inequalityαP(a, b) +(1- α)Q(a, b) < M(a, b) < βP(a, b) +(1- β)Q(a, b)holds for any a, b > 0 with a = b if and only if α≥ 1/2 and β≤ [π(√2 log(1 +√2)-1)]/[(√2π- 2) log(1 +√2)] = 0.3595, where M(a, b), Q(a,