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:	Sabour,KH, Kabbaj,S
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2017
Materias:	Functional equation Jensen quadratic additive func-tion semigroup
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100010
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spelling	oai:scielo:S0716-091720170001000102017-02-13Jensen’s and the quadratic functional equations with an endomorphismSabour,KHKabbaj,S Functional equation Jensen quadratic additive func-tion semigroup 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.36 n.1 20172017-03-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100010en10.4067/S0716-09172017000100010
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Functional equation Jensen quadratic additive func-tion semigroup
spellingShingle	Functional equation Jensen quadratic additive func-tion semigroup Sabour,KH Kabbaj,S Jensen’s and the quadratic functional equations with an endomorphism
description	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.
author	Sabour,KH Kabbaj,S
author_facet	Sabour,KH Kabbaj,S
author_sort	Sabour,KH
title	Jensen’s and the quadratic functional equations with an endomorphism
title_short	Jensen’s and the quadratic functional equations with an endomorphism
title_full	Jensen’s and the quadratic functional equations with an endomorphism
title_fullStr	Jensen’s and the quadratic functional equations with an endomorphism
title_full_unstemmed	Jensen’s and the quadratic functional equations with an endomorphism
title_sort	jensen’s and the quadratic functional equations with an endomorphism
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2017
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100010
work_keys_str_mv	AT sabourkh jensen8217sandthequadraticfunctionalequationswithanendomorphism AT kabbajs jensen8217sandthequadraticfunctionalequationswithanendomorphism
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Jensen&#8217;s and the quadratic functional equations with an endomorphism

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Jensen’s and the quadratic functional equations with an endomorphism