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Additive selections and the stability of the Cauchy functional equation

Published online by Cambridge University Press:  17 February 2009

Roman Badora ,
Roman Ger  and
Zsolt Páles
Roman Badora
Affiliation:
Institute of Mathematics, Silesian University, ul. Bankowa 14, PL-40-007 Katowice, Poland; e-mail: robadora@gate.math.us.edu.pl.
Roman Ger
Affiliation:
Institute of Mathematics, Silesian University, ul. Bankowa 14, PL-40-007 Katowice, Poland; e-mail: romanger@cto.us.edu.pl.
Zsolt Páles
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, H-4010 Debrecen, Pf. 12, Hungary; e-mail: 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.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 3 , January 2003 , pp. 323 - 337
Copyright
Copyright © Australian Mathematical Society 2003

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