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 $S$ is a semigroup and $\sigma$ an automorphism,…