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Kannappan-Wilson and Van Vleck-Wilson functional equations on semigroups
Youssef Aserrar, Elhoucien Elqorachi
Let be a semigroup, the center of and is an involutive automorphism. Our main results is that we describe the solutions of the Kannappan-Wilson fu…
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…
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}…