Abstract
In [7] H. Stetkær obtained the solutions of Van Vleck’s functional equation
for the sine where S is a semigroup, \({\tau}\) is an involution of S and z 0 is a fixed element in the center of S. The purpose of this paper is to determine the complex-valued solutions of the following extension of Van Vleck’s functional equation for the sine
where \({\mu : S\to \mathbb{C}}\) is a multiplicative function such that \({\mu (x\tau(x))=1}\) for all \({{x\in S}}\). Furthermore, we obtain the solutions of a variant of Van Vleck’s functional equation
for the sine on a monoid M, where \({\sigma}\) is an involutive automorphism of M.
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Belaid, B., Elhoucien, E. An extension of Van Vleck’s functional equation for the sine. Acta Math. Hungar. 150, 258–267 (2016). https://doi.org/10.1007/s10474-016-0630-1
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DOI: https://doi.org/10.1007/s10474-016-0630-1
Key words and phrases
- semigroup
- d’Alembert’s functional equation
- sine function
- Van Vleck
- involution
- multiplicative function
- homomorphism