A variant of the quadratic functional equation on semigroups.
Author
Fadli, B.
Zeglami, D.
Kabbaj, S.
Abstract
Let S be a semigroup, let H be an abelian group which is uniquely 2-divisible, and let σ be an involutive automorphism of S. We express the solutions f : S → H of the following variant of the quadratic functional equation
f(xy) + f(σ(y)x) = 2f(x) + 2f(y), x, y ∈ S,
in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation.