On Jensen’s and the quadratic functional equations with involutions

On Jensen’s and the quadratic functional equations with involutions

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 + &a...

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Autores principales: Fadli,B., Chahbi,A., El-Fassi,Iz., Kabbaj,S.
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2016
Materias:
Functional equation
Jensen
quadratic
additive func-tion
semigroup.
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000200006
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Sumario: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.

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