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
![∑n a+k- n∑ ak ∑n a+k-
f(b+) ≦ f(bk) ≦ f(b− )
1 k 1 i k](a040x.png) | (1) |
holds for all a,b ∈ R+n. Here n is a fixed integer > 1.
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