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.
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