- Tytuł:
- On the increasing solutions of the translation equation
- Autorzy:
- Brzdęk, Janusz
- Powiązania:
- https://bibliotekanauki.pl/articles/1310912.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
translation equation
linear order
increasing function
additive function - Opis:
- Let M be a non-empty set endowed with a dense linear order without the smallest and greatest elements. Let (G,+) be a group which has a non-trivial uniquely divisible subgroup. There are given conditions under which every solution F: M×G → M of the translation equation is of the form $F(a,x) = f^{-1}(f(a) + c(x))$ for a ∈ M, x ∈ G with some non-trivial additive function c: G → ℝ and a strictly increasing function f: M → ℝ such that f(M) + c(G) ⊂ f(M). In particular, a problem of J. Tabor is solved.
- Źródło:
-
Annales Polonici Mathematici; 1996, 64, 3; 207-214
0066-2216 - Pojawia się w:
- Annales Polonici Mathematici
- Dostawca treści:
- Biblioteka Nauki
Artykuł