A variant of the quadratic functional equation on semigroups

B. Fadli, D. Zeglami, S. Kabbaj


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 : SH of the following variant of the quadratic functional equation

f(xy) + f(σ(y)x) = 2f(x) + 2f(y), x, yS,

in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation.

Palabras clave

Symmetrized additive Cauchy equation ; Quadratic equation ; Additive function ; Semigroup

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