Jensen’s and the quadratic functional equations with an endomorphism
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) +...
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| Autores principales: | , |
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| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2017
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100010 |
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| Sumario: | 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. |
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