On a functional equation related to projections of abelian groups
Rätz, Jürg
In: aequationes mathematicae, 2005, vol. 70, no. 3, p. 279-297
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- Summary.: For an abelian group (G,+,0) we consider the functional equation (1) $$f:G \to G,\;f(x + y + f(y)) = f(x) + 2f(y)\quad (\forall x,y \in G),$$ most times together with the condition f(0)=0. A solution of (1) is always idempotent. Our main question is as to whether it must be additive, i.e., a projection of the abelian group G