Reference : Solving Chisini's functional equation
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/1192
Solving Chisini's functional equation
English
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Jun-2010
Aequationes Mathematicae
Springer
79
3
237-260
Yes (verified by ORBilu)
International
0001-9054
1420-8903
Basel
Switzerland
[en] Chisini's functional equation ; Chisini mean ; level surface mean ; Shepard's metric interpolation ; idempotency ; quasi-idempotency ; quasi-inverse function
[en] We investigate the n-variable real functions G that are solutions of the Chisini functional equation F(x) = F(G(x),...,G(x)), 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. We also provide necessary and sufficient conditions on F for the existence of continuous solutions and we show how to construct such a solution. We finally discuss a few applications of these results.
Mathematics Research Unit (FSTC)
University of Luxembourg - UL
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/1192
10.1007/s00010-010-0018-1
http://arxiv.org/abs/0903.1546

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