A note on an inequality for rearrangements

Christer Borell

Vol. 47 (1973), No. 1, 39–41

DOI: 10.2140/pjm.1973.47.39

Abstract

If a = (a₁,⋯,a_n) is a n-tuple of positive real numbers let a⁺ = (a₁⁺,⋯,a_n⁺) denote the rearrangement of a in increasing order and a⁻ = (a₁⁻,⋯,a_n⁻) 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.

Mathematical Subject Classification 2000

Primary: 05A20

Milestones

Received: 1 March 1972

Published: 1 July 1973