Abstract
Let S be a semigroup, and let \(\mathbb {F}\) be a quadratically closed field of characteristic ≠ 2 with identity element 1. We describe, in terms of multiplicative functions of S, the solutions \(f:S\rightarrow \mathbb {F}\) of the new functional equation
where \(\phi ,\varphi :S\rightarrow S\) are two endomorphisms that need not be involutive and \(\mu :S\rightarrow \mathbb {F}\) is a multiplicative map such that μ(xφ(x)) = 1 for all x ∈ S. Significant consequences of this result are presented.
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Ayoubi, M., Zeglami, D. A Functional Equation for the Cosine on Semigroups with Endomorphisms. Vietnam J. Math. 52, 149–157 (2024). https://doi.org/10.1007/s10013-022-00587-y
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DOI: https://doi.org/10.1007/s10013-022-00587-y