Jensen’s and the quadratic functional equations with an endomorphism

K. H. Sabour, S. Kabbaj

Resumen


We determine the solutions f : S → H of the generalized Jensen’s functional equation

f (x + y) + f (x + φ(y)) = 2f (x),    x,y ∈ S,

and the solutions f : S → H of the generalized quadratic functional equation

f (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.


Palabras clave


Functional equation; Jensen; quadratic; additive function; semigroup.

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Referencias


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DOI: http://dx.doi.org/10.4067/S0716-09172017000100010

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