Communications of the
Korean Mathematical Society CKMS

Let $S$ be a semigroup. We determine the complex-valued solutions of the following functional equation \[f(xy)+\mu (y)f(\sigma (y)x) = 2f(x)g(y),\ x,y\in S,\] where $\sigma:S\rightarrow S$ is an automorphism, and $\mu :S\rightarrow \mathbb{C}$ is a multiplicative function such that $\mu (x\sigma (x))=1$ for all $x\in S$.

Keywords: Semigroup, Wilson's equation, automorphism, multiplicative function

MSC numbers: Primary 39B52; Secondary 39B32