1. Equation $f(p(x)) = q(f(x))$ for given real functions $p$, $q$
- Creator:
- Kopeček, Oldřich
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- homomorphism of mono-unary algebras, functional equation, and strictly increasing continuous real functions
- Language:
- English
- Description:
- We investigate functional equations $f(p(x)) = q(f(x))$ where $p$ and $q$ are given real functions defined on the set ${\Bbb R}$ of all real numbers. For these investigations, we can use methods for constructions of homomorphisms of mono-unary algebras. Our considerations will be confined to functions $p, q$ which are strictly increasing and continuous on ${\Bbb R}$. In this case, there is a simple characterization for the existence of a solution of the above equation. First, we give such a characterization. Further, we present a construction of any solution of this equation if some exists. This construction is demonstrated in detail and discussed by means of an example.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public