ArticleOriginal scientific text
Title
On the increasing solutions of the translation equation
Authors 1
Affiliations
- Institute of Mathematics, Pedagogical University of Rzeszów, Rejtana 16a, 35-310 Rzeszów, Poland
Abstract
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 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.
Keywords
translation equation, linear order, increasing function, additive function
Bibliography
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- J. Tabor, Characterization of mixed iteration groups, to appear.