A new generalization of Wilson’s functional equation

Keywords: Wilson’s equation, Group, Semigroup involutive automorphism, Multiplicative function

Abstract

Let G be a group, let σ : G → G be an involutive automorphism and let χ1, χ2 : G → C∗ be two characters of G such that χ2(xσ(x)) = 1 for all x ∈ G. The aim of this paper is to describe the solutions f, g : G → C of the functional equation χ1(y)f (xy) + χ2(y)f (σ(y)x) = 2f (x)g(y), x,y ∈ G, in terms of characters and additive functions.

Author Biographies

Hajira Dimou, Ibn Tofail University.
Department of Mathematics.
Abdellatif Chahbi, Ibn Tofail University.
Department of Mathematics.
Samir Kabbaj, Ibn Tofail University.
Department of Mathematics.

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Published
2019-12-15
How to Cite
[1]
H. Dimou, A. Chahbi, and S. Kabbaj, “A new generalization of Wilson’s functional equation”, Proyecciones (Antofagasta, On line), vol. 38, no. 5, pp. 943-954, Dec. 2019.
Section
Artículos