A variant of the quadratic functional equation on semigroups.

Authors

  • B. Fadli IBN Tofail University.
  • D. Zeglami Moulay ISMAIL University.
  • S. Kabbaj IBN Tofail University.

Keywords:

Symmetrized additive cauchy equation, Quadratic equation, Additive function, Semigroup

Abstract

Let S be a semigroup, let H be an abelian group which is uniquely 2-divisible, and let σ be an involutive automorphism of S. We express the solutions f : SH of the following variant of the quadratic functional equation

f(xy) + f(σ(y)x) = 2f(x) + 2f(y), x, yS,

in terms of bi-additive maps and solutions of the symmetrized additive Cauchy equation.

Author Biographies

B. Fadli, IBN Tofail University.

Department of Mathematics, Faculty of Sciences.

D. Zeglami, Moulay ISMAIL University.

Department of Mathematics, E. N. S. A. M.

 

S. Kabbaj, IBN Tofail University.

Department of Mathematics, Faculty of Sciences.

 

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Published

2018-03-15

How to Cite

[1]
B. Fadli, D. Zeglami, and S. Kabbaj, “A variant of the quadratic functional equation on semigroups.”, Proyecciones (Antofagasta, On line), vol. 37, no. 1, pp. 45-55, Mar. 2018.

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Section

Artículos