Solution of Several Functional Equations on Nonunital Semigroups Using Wilson’s Functional Equations with Involution

Abstract EN

Let S be a nonunital commutative semigroup, σ : S → S an involution, and C the set of complex numbers.

In this paper, first we determine the general solutions f , g : S → C of Wilson’s generalizations of d’Alembert’s functional equations f x + y + f x + σ y = 2 f ( x ) g ( y ) and f x + y + f x + σ y = 2 g ( x ) f ( y ) on nonunital commutative semigroups, and then using the solutions of these equations we solve a number of other functional equations on more general domains.