caa a22 4500 605508070 CHVBK 20210128105158.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s00010-014-0306-2 doi (NATIONALLICENCE)springer-10.1007/s00010-014-0306-2 Rätz Jürg Mathematisches Institut der Universität Bern, Sidlerstrasse, 3012, Bern, Switzerland aut On the functional equation x + f ( y + f ( x )) [Elektronische Daten] y + f ( x + f ( y )), II [Jürg Rätz] For an abelian group (G,+,0) we consider the functional equation 1 $$f : G \to G, \,\, x + f(y + f(x)) = y + f(x + f(y)) \quad (\forall x, y \in G),\qquad \qquad\quad (1)$$ f : G → G , x + f ( y + f ( x ) ) = y + f ( x + f ( y ) ) ( ∀ x , y ∈ G ) , together with the condition 0 $$f(0) = 0. \qquad\qquad\qquad\qquad\qquad (0)$$ f ( 0 ) = 0 . The main question is that of existence of solutions of (1) $${\wedge}$$ ∧ (0), specifically in the case when G is the direct sum $${\mathbb{Z}_n^{(J)}}$$ Z n ( J ) of copies of a finite or infinite cyclic group (Theorems 3.2 and 4.20). Springer Basel, 2014 Abelian groups nationallicence composite functional equations nationallicence Aequationes mathematicae Springer Basel 89/1(2015-02-01), 169-186 0001-9054 89:1<169 2015 89 10 https://doi.org/10.1007/s00010-014-0306-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00010-014-0306-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rätz Jürg Mathematisches Institut der Universität Bern, Sidlerstrasse, 3012, Bern, Switzerland aut NATIONALLICENCE 773 0- Aequationes mathematicae Springer Basel 89/1(2015-02-01), 169-186 0001-9054 89:1<169 2015 89 10 SWISSBIB 509999557