Abel Functional Equation

[bo198214]

Solving these equations don't give the same results.

Hm, perhaps not the same but in certain cases equivalent results.

There is a bijection between the solutions of the Schröder equation and the Abel equation by
\( S(x)=c^{A(x)} \) and \( A(x)=\log_c(S(x)) \)
As you can see:
\( S(f(x))=c^{A(f(x))}=c^{A(x)+1}=cc^{A(x)}=cS(x) \)
and vice versa.

Of course one have to be a bit careful about negative values of S(x).