Yet another variant of the Drygas functional equation on groups

Yet another variant of the Drygas functional equation on groups

Let G be a group and C the field of complex numbers. Suppose σ1,σ 2 : G → G are endomorphisms satisfying the condition σi(σi(x)) = x for all x in G and for i = 1, 2. In this paper, we find the central solution f : G → C of the equation f (xy) +...

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Autor principal: Sahoo,Prasanna K
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2017
Materias:
Drygasfunctional equation;
group
Fréchet’s functional equation
involution
semigroup
Whitehead functional equation
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100002
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spelling oai:scielo:S0716-091720170001000022017-02-13Yet another variant of the Drygas functional equation on groupsSahoo,Prasanna K Drygasfunctional equation; group Fréchet’s functional equation involution semigroup Whitehead functional equation Let G be a group and C the field of complex numbers. Suppose σ1,σ 2 : G → G are endomorphisms satisfying the condition σi(σi(x)) = x for all x in G and for i = 1, 2. In this paper, we find the central solution f : G → C of the equation f (xy) + f (σi(y)x) =2f (x) + f (y) + f (σ2(y)) for all x,y ∈ G which is a variant of the Drygas functional equation with two involutions. Further, we present a generalization the above functional equation and determine its central solutions. As an application, using the solutions ofthe generalized equation, we determine the solutions f, g, h, k : GxG → C ofthefunc-tional equation f (pr, qs) + g(sp, rq) = 2f (p, q) + h(r, s) + k(s, r) when f satisfies the condition f (pr, qs) = f (rp, sq) for all p, q, r, s ∈ G.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=S0716-09172017000100002en10.4067/S0716-09172017000100002
institution Scielo Chile
collection Scielo Chile
language English
topic Drygasfunctional equation;
group
Fréchet’s functional equation
involution
semigroup
Whitehead functional equation
spellingShingle Drygasfunctional equation;
group
Fréchet’s functional equation
involution
semigroup
Whitehead functional equation
Sahoo,Prasanna K
Yet another variant of the Drygas functional equation on groups
description Let G be a group and C the field of complex numbers. Suppose σ1,σ 2 : G → G are endomorphisms satisfying the condition σi(σi(x)) = x for all x in G and for i = 1, 2. In this paper, we find the central solution f : G → C of the equation f (xy) + f (σi(y)x) =2f (x) + f (y) + f (σ2(y)) for all x,y ∈ G which is a variant of the Drygas functional equation with two involutions. Further, we present a generalization the above functional equation and determine its central solutions. As an application, using the solutions ofthe generalized equation, we determine the solutions f, g, h, k : GxG → C ofthefunc-tional equation f (pr, qs) + g(sp, rq) = 2f (p, q) + h(r, s) + k(s, r) when f satisfies the condition f (pr, qs) = f (rp, sq) for all p, q, r, s ∈ G.
author Sahoo,Prasanna K
author_facet Sahoo,Prasanna K
author_sort Sahoo,Prasanna K
title Yet another variant of the Drygas functional equation on groups
title_short Yet another variant of the Drygas functional equation on groups
title_full Yet another variant of the Drygas functional equation on groups
title_fullStr Yet another variant of the Drygas functional equation on groups
title_full_unstemmed Yet another variant of the Drygas functional equation on groups
title_sort yet another variant of the drygas functional equation on groups
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2017
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000100002
work_keys_str_mv AT sahooprasannak yetanothervariantofthedrygasfunctionalequationongroups
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