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Proyecciones (Antofagasta)

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Abstract

FADLI, B.; CHAHBI, A.; EL-FASSI, Iz.  and  KABBAJ, S.. On Jensen’s and the quadratic functional equations with involutions. Proyecciones (Antofagasta) [online]. 2016, vol.35, n.2, pp.213-223. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172016000200006.

We determine the Solutions f : S → H of the generalized Jensen’s functional equation f( x + σ(y)) + f( x + τ(y)) = 2f(x), x , y S and the solutions f : S H of the generalized quadratic functional equation f ( x + σ(y)) + f (x + τ(y)) = 2f (x) + 2f (y),    x, y S, where S is a commutative semigroup, H is an abelian group (2-torsion free in the first equation and uniquely 2-divisible in the second) and σ, τ are two involutions of S.

Keywords : Functional equation; Jensen; quadratic; additive func-tion; semigroup..

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