Positivity (2015) 19:251–288
Some pretty simple inequalities I
Grahame Bennett · Karl-G. Grosse-Erdmann
Received: 21 December 2013 / Accepted: 10 May 2014 / Published online: 6 June 2014
© Springer Basel 2014
Abstract We show that a great variety of inequalities are best understood via an
extrapolation principle: they hold true simply because they are valid on a small set of
test sequences (or functions). The real challenge then is to determine the best constant.
This invariably leads to interesting discussions of monotonicities of sequences.
Keywords Extrapolation principle · Cone · Sums of powers · Boas’s inequality ·
Mathematics Subject Classiﬁcation (2000) 26D15
We study inequalities of the type
≤ K B x
(and their integral analogues). Here, A and B are ﬁxed matrices with non-negative
entries, and the inequality is to hold for all sequences x belonging to some cone C of
The research of the second author was supported by the FNRS, Belgium.
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA
K.-G. Grosse-Erdmann (
Département de Mathématique, Institut Complexys, Université de Mons, 7000 Mons, Belgium