A variant of the quadratic functional equation on semigroups.
Keywords:Symmetrized additive cauchy equation, Quadratic equation, Additive function, Semigroup
AbstractLet S be a semigroup, let H be an abelian group which is uniquely 2-divisible, and let ? 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(?(y)x) = 2f(x) + 2f(y), x, y ? S, in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation.
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