Equation $f(p(x)) = q(f(x))$ for given real functions $p$, $q$

Title:

Equation $f(p(x)) = q(f(x))$ for given real functions $p$, $q$

Creator:

Kopeček, Oldřich

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:d8fe2d3b-c2d7-4cdd-a1bb-d4924de6b80a
uuid:d8fe2d3b-c2d7-4cdd-a1bb-d4924de6b80a

Subject:

homomorphism of mono-unary algebras, functional equation, and strictly increasing continuous real functions

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1011-1032

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:4

Harvested from:

CDK

Metadata only:

false