Abstract: | 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]whereAn,Gn, andHnare arithmetic, geometric, and harmonic means, respectively, of positive numbersx1, x2,…,xn;A′nandG′nare arithmetic and geometric means of a sequence 1−x1, 1−x2,…,1−xnwithxi∈(0, 12],i=1, 2,…,n. |