Abstract :
[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.
Name of the research project :
F1R-MTH-PUL-09MRDO > MRDO > 01/01/2009 - 31/12/2011 > MARICHAL Jean-Luc
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