| Title:
|
Equation $f(p(x)) = q(f(x))$ for given real functions $p$, $q$ (English) |
| Author:
|
Kopeček, Oldřich |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
4 |
| Year:
|
2012 |
| Pages:
|
1011-1032 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
homomorphism of mono-unary algebras |
| Keyword:
|
functional equation |
| Keyword:
|
strictly increasing continuous real functions |
| MSC:
|
08A60 |
| MSC:
|
65Q20 |
| MSC:
|
97I70 |
| idZBL:
|
Zbl 1274.08022 |
| idMR:
|
MR3010254 |
| DOI:
|
10.1007/s10587-012-0061-2 |
| . |
| Date available:
|
2012-11-10T21:39:14Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143042 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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