Assume that (X,+) are commutative groups, and C is a subset of X fulfilling the conditions C+C ⊆ C and C-C = X. A function f: X→Y is called C-additive function if it satisfies functional equation f(x+y) = f(x) + f{y), for all x,y∈X such that y-x∈C∪(-C)∪{0}. In [1, Theorem 8.4] has been proved that every C-additive function f: X→Y is additive. In the proof the comutativity has been essentially used. Here we present a simple proof of an analogous statement in the case of arbitrary groups.
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Vol. 14 (2000)
Published: 2000-09-29
10.1515/amsil
English