A variant of the quadratic functional equation on semigroups
Abstract: Let S be a semigroup, let H be an abelian group which is uniquely 2-divisible, and let σ be an involutive automorphism of S. We express the solutions : S → H of the following variant of the quadratic functional equation (xy)+𝑓(σ(y)x)=2𝑓(x...
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| Autores principales: | , , |
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| Lenguaje: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2018
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| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000100045 |
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| Sumario: | Abstract: Let S be a semigroup, let H be an abelian group which is uniquely 2-divisible, and let σ be an involutive automorphism of S. We express the solutions : S → H of the following variant of the quadratic functional equation (xy)+𝑓(σ(y)x)=2𝑓(x)+2𝑓(y), x,y ∈ S, in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation. |
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