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Solution of Several Functional Equations on Nonunital Semigroups Using Wilson's Functional Equations with Involution
2014
Abstract and Applied Analysis
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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