Solutions and stability of a variant of Wilson's functional equation

Abstract: In this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson's functional equation (E): 𝑓(xy)+χ(y)𝑓(σ(y)x)=2𝑓(x)g(y), x,y ∈ G, where G is a group, σ is an invo...

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Autores principales:	Elqorachi,Elhoucien, Redouani,Ahmed
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2018
Materias:	Semigroup-Involution D'Alembert's equation Wilson's equation Automorphism Homomorphism Multiplicative function Hyers-Ulam stability Superstability
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000200317
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spelling	oai:scielo:S0716-091720180002003172018-05-29Solutions and stability of a variant of Wilson's functional equationElqorachi,ElhoucienRedouani,Ahmed Semigroup-Involution D'Alembert's equation Wilson's equation Automorphism Homomorphism Multiplicative function Hyers-Ulam stability Superstability Abstract: In this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson's functional equation (E): 𝑓(xy)+χ(y)𝑓(σ(y)x)=2𝑓(x)g(y), x,y ∈ G, where G is a group, σ is an involutive morphism of G and χ is a character of G. (a) We solve (E) when σ is an involutive automorphism, and we obtain some properties about solutions of (E) when σ is an involutive anti-automorphism. (b) We obtain the Hyers Ulam stability of equation (E). As an application, we prove the superstability of the functional equation (xy)+χ(y) 𝑓(σ(y)x)=2 𝑓(x) 𝑓(y), x,y ∈ G.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.37 n.2 20182018-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000200317en10.4067/S0716-09172018000200317
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Semigroup-Involution D'Alembert's equation Wilson's equation Automorphism Homomorphism Multiplicative function Hyers-Ulam stability Superstability
spellingShingle	Semigroup-Involution D'Alembert's equation Wilson's equation Automorphism Homomorphism Multiplicative function Hyers-Ulam stability Superstability Elqorachi,Elhoucien Redouani,Ahmed Solutions and stability of a variant of Wilson's functional equation
description	Abstract: In this paper we will investigate the complex-valued solutions and stability of the generalized variant of Wilson's functional equation (E): 𝑓(xy)+χ(y)𝑓(σ(y)x)=2𝑓(x)g(y), x,y ∈ G, where G is a group, σ is an involutive morphism of G and χ is a character of G. (a) We solve (E) when σ is an involutive automorphism, and we obtain some properties about solutions of (E) when σ is an involutive anti-automorphism. (b) We obtain the Hyers Ulam stability of equation (E). As an application, we prove the superstability of the functional equation (xy)+χ(y) 𝑓(σ(y)x)=2 𝑓(x) 𝑓(y), x,y ∈ G.
author	Elqorachi,Elhoucien Redouani,Ahmed
author_facet	Elqorachi,Elhoucien Redouani,Ahmed
author_sort	Elqorachi,Elhoucien
title	Solutions and stability of a variant of Wilson's functional equation
title_short	Solutions and stability of a variant of Wilson's functional equation
title_full	Solutions and stability of a variant of Wilson's functional equation
title_fullStr	Solutions and stability of a variant of Wilson's functional equation
title_full_unstemmed	Solutions and stability of a variant of Wilson's functional equation
title_sort	solutions and stability of a variant of wilson's functional equation
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2018
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172018000200317
work_keys_str_mv	AT elqorachielhoucien solutionsandstabilityofavariantofwilsonsfunctionalequation AT redouaniahmed solutionsandstabilityofavariantofwilsonsfunctionalequation
_version_	1718439835243380736

Solutions and stability of a variant of Wilson's functional equation

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