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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

FADLI, B.; ZEGLAMI, D.  and  KABBAJ, S.. A variant of the quadratic functional equation on semigroups. Proyecciones (Antofagasta) [online]. 2018, vol.37, n.1, pp.45-55. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172018000100045.

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)+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.

Keywords : Symmetrized additive Cauchy equation; quadratic equation; additive function; semigroup..

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