3 citations · 10 across the 17 of their papers we have counts for
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A variant of Wilson's functional equation on semigroups
Youssef Aserrar, Abdellatif Chahbi, Elhoucien Elqorachi
We determine the complex-valued solutions of the following functional equation \[f(xy)+μ(y)f(σ(y)x) = 2f(x)g(y),\quad x,y\in S,\] where is a semigroup and an automorphism,…
A d'Alembert type functional equation on semigroups
Youssef Aserrar, Elhoucien Elqorachi
We treat two related trigonometric functional equations on semigroups. First we solve the -sine subtraction law \[μ(y) k(x σ(y))=k(x) l(y)-k(y) l(x), \quad x, y \in S,\] for $k,…
A generalization of the cosine addition law on semigroups
Youssef Aserrar, Elhoucien Elqorachi
Our main result is that we describe the solutions of the functional equation \[g(xσ(y))=g(x)g(y)-f(x)f(y)+αf(xσ(y)),\quad x,y\in S,\] where is a se…
Five Trigonometric addition laws on semigroups
Youssef Aserrar, Elhoucien Elqorachi
In this paper, we determine the complex-valued solutions of the following functional equations \[g(xσ(y)) = g(x)g(y)+f(x)f(y),\quad x,y\in S,\]\[f(xσ(y)) = f(x)g(y)+f(y)g(x),\quad…
A system of cosine-sine functional equations on a semigroup generated by its squares
Omar Ajebbar, Elhoucien Elqorachi
Given a semigroup generated by its squares, we determine the complex-valued solutions of the following system of cosine-sine functional equations \begin{align*} f(xy)=f(x)g_{1}…