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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

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

http://dx.doi.org/10.4067/S0716-09172016000200006 

Proyecciones Journal of Mathematics Vol. 35, No 2, pp. 213-223, June 2016. Universidad Católica del Norte Antofagasta - Chile

On Jensen’s and the quadratic functional equations with involutions

B. Fadli

A. Chahbi 

Iz. El-Fassi 

S. Kabbaj 

IBN Tofail University, Morocco 


ABSTRACT

We determine the Solutions f : S → H of the generalized Jensen’s functional equation

f( x + σ(y)) + f( x + τ(y)) = 2f(x), x , y∈ S

and the solutions f : S → H of the generalized quadratic functional equation

f ( x + σ(y)) + f (x + τ(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 σ, τ are two involutions of S.

Subjclass [2010] : Primary 39B52.

Keywords : Functional equation, Jensen, quadratic, additive func-tion, semigroup.


REFERENCES

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B. Fadli

Department of Mathematics,

Faculty of Sciences,

Ibn Tofail University,

B. P. 14000. Kenitra,

Morocco

e-mail : himfadli@gmail.com

A.    Chahbi

Department of Mathematics,

Faculty of Sciences,

Ibn Tofail University,

B.    P. 14000. Kenitra,

Morocco

e-mail : abdellatifchahbi@gmail.com

Iz. EL-Fassi

Department of Mathematics,

Faculty of Sciences,

Ibn Tofail University,

B. P. 14000. Kenitra,

Morocco

e-mail : izidd-math@hotmail.fr

S. Kabbaj

Department of Mathematics,

Faculty of Sciences,

Ibn Tofail University,

B. P. 14000. Kenitra,

Morocco

e-mail : samkabbaj@yahoo.fr

Received : March 2016. Accepted : May 2016

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