Solution of Several Functional Equations on Nonunital Semigroups Using Wilson’s Functional Equations with Involution
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 fx+y+fx+σy=2f(x)g(y) and fx+y+fx+σy=2g(x)f(y) on nonunital commutative...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/463918 |
| Summary: | 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 fx+y+fx+σy=2f(x)g(y)
and fx+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. |
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| ISSN: | 1085-3375 1687-0409 |