On the functional equation x + f ( y + f ( x ))
y + f ( x + f ( y )), II
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| 024 | 7 | 0 | |a 10.1007/s00010-014-0306-2 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0306-2 | ||
| 100 | 1 | |a Rätz |D Jürg |u Mathematisches Institut der Universität Bern, Sidlerstrasse, 3012, Bern, Switzerland |4 aut | |
| 245 | 1 | 0 | |a On the functional equation x + f ( y + f ( x )) |h [Elektronische Daten] |b y + f ( x + f ( y )), II |c [Jürg Rätz] |
| 520 | 3 | |a 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). | |
| 540 | |a Springer Basel, 2014 | ||
| 690 | 7 | |a Abelian groups |2 nationallicence | |
| 690 | 7 | |a composite functional equations |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 169-186 |x 0001-9054 |q 89:1<169 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0306-2 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0306-2 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Rätz |D Jürg |u Mathematisches Institut der Universität Bern, Sidlerstrasse, 3012, Bern, Switzerland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 169-186 |x 0001-9054 |q 89:1<169 |1 2015 |2 89 |o 10 | ||
| 986 | |a SWISSBIB |b 509999557 | ||