Abstract
Let A be a subgroup of a commutative group (G, +) and P be a quadratically closed field. We give the full description of all pairs of functions f : G → P and g : A → P such that f(x + y) + f(x − y) = 2f(x)g(y) for (x, y) ∈ G × A.
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Bahyrycz, A., Brzdȩk, J. A note on d’Alembert’s functional equation on a restricted domain. Aequat. Math. 88, 169–173 (2014). https://doi.org/10.1007/s00010-013-0246-2
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DOI: https://doi.org/10.1007/s00010-013-0246-2