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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.35 no.2 Antofagasta June 2016

http://dx.doi.org/10.4067/S0716-09172016000200002 

Proyecciones Journal of Mathematics Vol. 35, No 2, pp. 159-176, June 2016. Universidad Católica del Norte Antofagasta - Chile

A generalization of Drygas functional equation

A. Charifi M. Almahalebi 

S. Kabbaj 

Ibn Tofail University

Morocco 


ABSTRACT

We obtain the Solutions of the following Drygas functional equation

λ ∈Φ f (x + λy + aλ ) = κf(x)+ ∑ λ ∈Φ f(λy), x, y ∈ S

where S is an abelian semigroup, G is an abelian group, f ∈ GS, Φ is a finite automorphism group of S with order k, and aλ ∈ S, λ∈Φ.

Subjclass 2010 Mathematics Subject Classification (MSC) :

20B25; 39B52; 47B39; 65Q20.

Keywords and Phrases : Automorphism group; difference opera-tor; Drygas functional equation.


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A. Charifi

Department of Mathematics, Faculty of Sciences,

Ibn Tofail University,

BP: 133, 14000,

Kenitra,

Morocco

e-mail : charifi2000@yahoo.fr

M. Almahalebi

Department of Mathematics, Faculty of Sciences,

Ibn Tofail University,

BP: 133, 14000,

Kenitra,

Morocco

e-mail : muaadh1979@hotmail.fr

S. Kabbaj

Department of Mathematics, Faculty of Sciences,

Ibn Tofail University,

BP: 133, 14000,

Kenitra,

Morocco

e-mail : samkabbaj@yahoo.fr

Received : April 2015. Accepted : April 2016

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