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 Variants of Wilson's functional equation on semigroups Commun. Korean Math. Soc.Published online March 10, 2020 omar AJEBBAR and Elhoucien Elqorachi Departement of Mathematics, Ibn Zohr University, Faculty of Sciences, Agadir, Morocco Abstract : Given a semigroup $S$ generated by its squares equipped with an involutive automorphism $\sigma$ and a multiplicative function $\mu:S\to\mathbb{C}$ such that $\mu(x\sigma(x))=1$ for all $x\in S$, we determine the complex-valued solutions of the following functional equations \begin{equation*}f(xy)+\mu(y)f(\sigma(y)x)=2f(x)g(y),\, x,y\in S\end{equation*} and \begin{equation*}f(xy)+\mu(y)f(\sigma(y)x)=2f(y)g(x),\, x,y\in S.\end{equation*} Keywords : Semigroup; involutive automorphism; Multiplicative function; d'Alembert equation; Wilson equation. MSC numbers : Primary 39B52; Secondary 39B32. Full-Text :