On the increasing solutions of the translation equation

• Autorzy: Janusz Brzdęk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

translation equation; linear order; increasing function; additive function

Kategorie tematyczne

• 39B52: Equations for functions with more general domains and/or ranges

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 64
• Numer: 3
• Strony: 207-214

Daty

wydano

1996

otrzymano

1991-11-16

poprawiono

1995-11-08

Twórcy

autor

Janusz Brzdęk

• Institute of Mathematics, Pedagogical University of Rzeszów, Rejtana 16a, 35-310 Rzeszów, Poland

Bibliografia

• [1] U. Abel, Sur les groupes d'itération monotones, Publ. Math. Debrecen 29 (1982), 65-71.
• [2] J. Aczél, L. Kalmár et J. G. Mikusiński, Sur l'équation de translation, Studia Math. 12 (1951), 112-116.
• [3] A. Grzegorczyk and J. Tabor, Monotonic solutions of the translation equation, Ann. Polon. Math. 43 (1983), 253-260.
• [4] J. Tabor, Characterization of mixed iteration groups, to appear.