Abstract
We investigate the solvability of functional equations f(p(x)) = q(f(x)) for given functions p and q which are partially or completely defined on the set of all real numbers. For these investigations, we use methods for constructions of homomorphisms of mono-unary algebras. We can present a simple characterisation of solvability of the above equation in the case that p, q are strictly increasing and continuous functions. It gives, on the one hand, a practical use for a class of functional equations. On the other hand, it is a contribution to questions on topological conjugacy of monotonous real functions.
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Kopeček, O. On solvability of f(p(x)) = q(f(x)) for given real functions p, q . Aequat. Math. 90, 471–494 (2016). https://doi.org/10.1007/s00010-015-0392-9
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DOI: https://doi.org/10.1007/s00010-015-0392-9