Jensen’s and the quadratic functional equations with an endomorphism

• Sabour, K. H. ^[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. 36, Nº. 1, 2017, págs. 187-194
• Idioma: inglés
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• Resumen

  • We determine the solutions f : S → H of the generalized Jensen’s functional equationf (x + y) + f (x + φ(y)) = 2f (x),    x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equationf (x + y) + f (x + φ(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 φ is an endomorphism of S.