The aim of the present paper is to show that there are monotonic continuous functionsh(t), k(t), p(t), q(t) such that[formula]and[formula]whereA_n,G_n, andH_nare arithmetic, geometric, and harmonic means, respectively, of positive numbersx₁, x₂,…,x_n;A′_nandG′_nare arithmetic and geometric means of a sequence 1−x₁, 1−x₂,…,1−x_nwithx_i(0, ],i=1, 2,…,n.