descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 2018 English Publisher:Universidad Catolica del Norte - ChileJournal:Proyecciones (Antofagasta), volume 37, pages 45-55 (issn: 0716-0917,

Authors: Fadli, B.; Zeglami, D.; Kabbaj, S.;

doi: 10.4067/s0716-09172018000100045 , 10.22199/issn.0717-6279-2779

A variant of the quadratic functional equation on semigroups

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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.

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Keywords

additive function, semigroup., Symmetrized additive Cauchy equation, quadratic equation

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