If a = (a1,⋯,an) is a n-tuple of
positive real numbers let a+= (a1+,⋯,an+) denote the rearrangement of a in
increasing order and a−= (a1−,⋯,an−) the rearrangement of a in decreasing order.
In this note a characterization is given for those functions f : R+→ R such
that
(1)
holds for all a,b ∈ R+n. Here n is a fixed integer > 1.