ANZIAM J.
44 (2003), 323-337
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Additive selections and the stability of the Cauchy functional equation
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Roman Ger
Institute of Mathematics
Silesian University
ul. Bankowa 14
PL-40-007 Katowice
Poland
romanger@cto.us.edu.pl
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Zsolt Páles
Institute of Mathematics and Informatics
University of Debrecen
H-4010 Debrecen, Pf. 12
Hungary
pales@math.klte.hu
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Abstract
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The main result of this paper offers a necessary
and sufficient condition for the existence of an
additive selection of a weakly compact convex
set-valued map defined on an amenable semigroup.
As an application, we obtain characterisations of
the solutions of several functional inequalities,
including that of quasi-additive functions.
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