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

Jaeyoung Chung, Prasanna K. Sahoo
2014 Abstract and Applied Analysis  
LetSbe a nonunital commutative semigroup,σ:S→San involution, andCthe set of complex numbers. In this paper, first we determine the general solutionsf,g:S→Cof Wilson's generalizations of d'Alembert's functional equations fx+y+fx+σy=2f(x)g(y)andfx+y+fx+σy=2g(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.
doi:10.1155/2014/463918 fatcat:3boewwky7renfk2kfaeeetjcnm