Jensen’s and the quadratic functional equations with an endomorphism

Authors

  • K. H. Sabour IBN Tofail University.
  • Samir Kabbaj IBN Tofail University.

DOI:

https://doi.org/10.4067/S0716-09172017000100010

Keywords:

Functional equation, Jensen, quadratic, additive function, semigroup

Abstract

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 Biographies

K. H. Sabour, IBN Tofail University.

Department of Mathematics, Faculty of Sciences.

Samir Kabbaj, IBN Tofail University.

Department of Mathematics, Faculty of Sciences.

References

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[2] B. Fadli, A. Chahbi, Iz. EL-Fassi and S. Kabbaj, On Jensen’s and the quadratic functional equations with involutions, Proyecciones (Antofagasta) 35 (2), pp. 213-223, (2016).

[3] B. Fadli, S. Kabbaj, Kh. Sabour and D. Zeglami, Functional equations on semigroups with an endomorphism, Acta Math. Hungar. (2016), DOI 10.1007/s10474-016-0635-9.

[4] B. Fadli, D. Zeglami and S. Kabbaj, A variant of Jensen’s functional equation on semigroups, Demonstratio Math., to appear.

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[14] H. Stetkær, Functional Equations on Groups, World Scientific Publishing Co, Singapore, (2013).

Published

2017-04-06

How to Cite

[1]
K. H. Sabour and S. Kabbaj, “Jensen’s and the quadratic functional equations with an endomorphism”, Proyecciones (Antofagasta, On line), vol. 36, no. 1, pp. 187-194, Apr. 2017.

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