Vol. 47, No. 1, 1973

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A note on an inequality for rearrangements

Christer Borell

Vol. 47 (1973), No. 1, 39–41
Abstract

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
(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
Authors
Christer Borell