Given integers ,,
such that (,,
) 6= (k,2k, k) for all k 2 Z, we will establish a criterion for the
existence of the general solution of the alternative Jensen’s functional equation of the form f (x y1)2f (x)+ f (x y) =
0 or f (x y1)+ f (x)+
f (x y) = 0, where f is a mapping from a group (G, ) to a uniquely divisible abelian group
(H,+). We also find the general solution in the case when G is a cyclic group.

Keywords

alternative equation, Jensen’s functional equation, additive function