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The Chisini mean revisited
Marichal, Jean-Luc
2009In González, Manuel; Mayor, Gaspar; Suner, Jaume et al. (Eds.) Proc. 5th Int. Summer School on Aggregation Operators and their Applications (AGOP 2009)
Peer reviewed
 

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Keywords :
Chisini's functional equation; Chisini mean; aggregation; idempotency; quasi-idempotency
Abstract :
[en] We investigate the $n$-variable real functions $\G$ that are solutions of the functional equation $\F(\bfx)=\F(\G(\bfx),\ldots,\G(\bfx))$, where $\F$ is a given function of $n$ real variables. We provide necessary and sufficient conditions on $\F$ for the existence and uniqueness of solutions. When $\F$ is nondecreasing in each variable, we show in a constructive way that if a solution exists then a nondecreasing and idempotent solution always exists. Such solutions, called Chisini means, are then thoroughly investigated.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-CONFERENCE-2010-404
Author, co-author :
Marichal, Jean-Luc ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
The Chisini mean revisited
Publication date :
2009
Event name :
5th Int. Summer School on Aggregation Operators and their Applications (AGOP 2009)
Event organizer :
Gaspar Mayor
Event place :
Palma de Mallorca, Spain
Event date :
from 06-07-2009 to 10-07-2009
Audience :
International
Main work title :
Proc. 5th Int. Summer School on Aggregation Operators and their Applications (AGOP 2009)
Editor :
González, Manuel
Mayor, Gaspar
Suner, Jaume
Torrens, Joan
Publisher :
Edicions UIB. Cas Jai. Campus Universitari, Universitat de Illes Balears, Spain
ISBN/EAN :
978-84-8384-101-3
Pages :
161-166
Peer reviewed :
Peer reviewed
Name of the research project :
F1R-MTH-PUL-09MRDO > MRDO > 01/01/2009 - 31/12/2011 > MARICHAL Jean-Luc
Funders :
University of Luxembourg - UL
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since 28 September 2013

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