A variant of the quadratic functional equation on semigroups

摘要

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 : S → H of the following variant of the quadratic functional equation (xy)+??(σ(y)x)=2??(x)+2??(y), x,y ∈ S, in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation.