- Tytuł:
- Iteration groups, commuting functions and simultaneous systems of linear functional equations
- Autorzy:
- Matkowski, J.
- Powiązania:
- https://bibliotekanauki.pl/articles/255342.pdf
- Data publikacji:
- 2008
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
iteration group
commuting functions
functional equations
functional inequalities - Opis:
- Let (ƒt)t∈R be a measurable iteration group on an open interval I. Under some conditions, we prove that the inequalies g o ƒa ≤ ƒa o g and g o ƒb ≤ ƒb o g for some a, b ∈ R imply that g must belong to the iteration group. Some weak conditions under which two iteration groups have to consist of the same elements are given. An extension theorem of a local solution of a simultaneous system of iterative linear functional equations is presented and applied to prove that, under some conditions, if a function g commutes in a neighbourhood of ƒ with two suitably chosen elements ƒa and ƒb of an iteration group of ƒ then, in this neighbourhood, g coincides with an element of the iteration group. Some weak conditions ensuring equality of iteration groups are considered.
- Źródło:
-
Opuscula Mathematica; 2008, 28, 4; 529-539
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł