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

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  • Jaeyoung Chung
  • Prasanna K. Sahoo

Abstract

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 + σy) = 2f(x)g(y) and f(x + y) + f(x + 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.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:463918
DOI: 10.1155/2014/463918
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