On Jensen’s and the quadratic functional equations with involutions

• Fadli, Brahim ^[1] ; Chahbi, Abdellatif ^[1] ; El-Fassi, Iz-Iddine ^[1] ; Kabbaj, Samir ^[1]
  1. [1] Université Ibn-Tofail

     Université Ibn-Tofail

     Kenitra, Marruecos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 35, Nº. 2, 2016, págs. 213-223
• Idioma: inglés
• DOI: 10.4067/S0716-09172016000200006
• Enlaces
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• Resumen

  • We determine the Solutions f : S → H of the generalized Jensen’s functional equationf( x + σ(y)) + f( x + τ(y)) = 2f(x), x , y∈ Sand the solutions f : S → H of the generalized quadratic functional equationf ( 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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