On the solution of functional equations of Wilson's type on monoids.
Author
El-Fassi, Iz-iddine
Chahbi, Abdellatif
Kabbaj, Samir
Abstract
Let S be a monoid, C be the set of complex numbers, and let σ,τ ∈ Antihom(S,S) satisfy τ ○ τ =σ ○ σ= id. The aim of this paper is to describe the solution ⨍,g: S → C of the functional equation
⨍(xσ(y)) + ⨍(τ(y)x) = 2f(x)g(y), x, y ∈ S,
in terms of multiplicative and additive functions. Let S be a monoid, C be the set of complex numbers, and let σ,τ ∈ Antihom(S,S) satisfy τ ○ τ =σ ○ σ= id. The aim of this paper is to describe the solution ⨍,g: S → C of the functional equation
in terms of multiplicative and additive functions.