" What about equation x = g(x ,f(x) ) ? "


Voil? , suppose g(x ,y) R^2-> R ; f:R->R continuous .

What can we infere about {g,f} ?

I 've tried to use formal opposite iterates:
g(x ,y) = m ^ [ n(x) ] (y)
f(x) = m ^ [ - n(x)] (x) (1)
(cranky writing for n(x) not integer ! ).

if it exists phi(x) , solution of Abel equation such as
phi( m(x) ) = phi(x) +1 , phi invertible ,

We obtain a "clean " expression :
g(x ,y) = phi ^ - 1( n(x) + phi(y) )
f(x) = phi ^ - 1( - n(x) + phi(x) ) (2)
n(x) any continuous real function .
Have you got other ideas or examples on mind ?
Please , give your comments ,

With my Best regards, Alain.

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