On the increasing solutions of the translation equation

Janusz Brzdęk. "On the increasing solutions of the translation equation." Annales Polonici Mathematici 64.3 (1996): 207-214. <http://eudml.org/doc/270001>.

@article{JanuszBrzdęk1996,
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 $F(a,x) = f^\{-1\}(f(a) + c(x))$ 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.},
author = {Janusz Brzdęk},
journal = {Annales Polonici Mathematici},
keywords = {translation equation; linear order; increasing function; additive function; dense linear order; group; uniquely divisible subgroup},
language = {eng},
number = {3},
pages = {207-214},
title = {On the increasing solutions of the translation equation},
url = {http://eudml.org/doc/270001},
volume = {64},
year = {1996},
}

TY - JOUR
AU - Janusz Brzdęk
TI - On the increasing solutions of the translation equation
JO - Annales Polonici Mathematici
PY - 1996
VL - 64
IS - 3
SP - 207
EP - 214
AB - 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.
LA - eng
KW - translation equation; linear order; increasing function; additive function; dense linear order; group; uniquely divisible subgroup
UR - http://eudml.org/doc/270001
ER -