A note on Wilson’s functional equation. (English) Zbl 1373.39018
Summary: Let \(S\) be a semigroup, and \(\mathbb {F}\) a field of characteristic \(\neq 2\). If the pair \(f,g:S \rightarrow \mathbb {F}\) is a solution of Wilson’s \(\mu \)-functional equation such that \(f \neq 0\), then \(g\) satisfies d’Alembert’s \(\mu \)-functional equation.
MSC:
| 39B32 | Functional equations for complex functions |
| 39B52 | Functional equations for functions with more general domains and/or ranges |
References:
| [1] | Bouikhalene, B., Elqorachi, E.: Stability of a generalization of Wilson’s equation. Aequationes Math. 90(3), 517-525 (2016) · Zbl 1346.39039 · doi:10.1007/s00010-015-0356-0 |
| [2] | Ebanks, B.R., Stetkær, H.: On Wilson’s functional equations. Aequationes Math. 89(2), 339-354 (2015) · Zbl 1323.39020 · doi:10.1007/s00010-014-0287-1 |
| [3] | Kaczmarz, S.: Sur l’équation fonctionelle \[f(x) + f(x +y) = \phi (y)f(x+ \tfrac{y}{2})\] f(x)+f(x+y)=ϕ(y)f(x+y2). Fund. Math. 6, 122-129 (1924) · JFM 50.0183.02 · doi:10.4064/fm-6-1-122-129 |
| [4] | Stetkær, H.: A link between Wilson’s and d’Alembert’s functional equations. Aequationes Math. 90(2), 407-409 (2016) · Zbl 1344.39012 · doi:10.1007/s00010-015-0336-4 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
