In this note we give the general solution of the functional equation
f(x) f(x+y) = f(y)2 f(x−y)2 g(y), x,y∈G,
and all the solutions of
f(x) f(x+y) = f(y)2 f(x−y)2 g(x) , x,y∈G,
with the additional supposition g(x) ≠ 0 for all x∈G. In both cases G denotes an arbitrary group written additively and f,g: G→ℝ are the unknown functions.
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Vol. 21 (2007)
Published: 2007-09-28
10.1515/amsil
English