D’Alembert’s and Wilson’s equations on semigroups

Abstract

In this paper we consider a generalization of d’Alembert’s equation and Wilson’s equation on commutative semigroups using only the semigroup operation, ie. we consider the functional equation h(x+2y)+h(x)=2f(y)h(x+y),x,y∈S,where f, h: S→ K, (S, +) is a commutative semigroup, K is a quadratically closed field, charK≠2.