In the paper The solvability of \(f(p(x)) = q(f(x))\) for given strictly monotonous continuous real functions p, q. Aequat. Math. 96, 901–925 (2022). https://doi.org/10.1007/s00010--02--00901-6, we solved the problem of the solvability of the mentioned equation \(f(p(x)) = q(f(x))\) . From the theory of mono-unary algebras from the 70s it follows that it is possible to find any solution of this equation if it exists. Behind this is a construction for mono-unary algebras. If we limit ourselves to strictly increasing (continuous) functions p, q then this construction can be reduced in such a way that it can be used as an algorithm for computations of solutions of \(f(p(x)) = q(f(x))\) .
