Abstract
The functional equation
(introduced by the first author in a competition model) is considered. The main result says that a function \({f : \mathbb{R} \rightarrow \mathbb{R}}\) satisfies this equation if, and only if, \({f = {\rm tanh} \circ \, \alpha \circ {\rm tan}^{-1}}\) , where \({\alpha : \mathbb{R} \rightarrow \mathbb{R}}\) is an additive function.
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References
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Kahlig, P., Matkowski, J. On a functional equation related to competition. Aequat. Math. 87, 301–308 (2014). https://doi.org/10.1007/s00010-013-0215-9
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DOI: https://doi.org/10.1007/s00010-013-0215-9