Abstract
The functional equation related to competition ([2])
for y = cx with a fixed c > 0, leads to the equation
The case c = 1 (a first order iterative functional equation) was treated in [3]. In this paper we consider the case c ≠ 1 (when the equation is of the second order). We show that a function \({f:\mathbb{R} \rightarrow \mathbb{R},\,f\left( 0\right) =0}\), differentiable at the point 0 satisfies this functional equation iff there is a real p such that \({f=\tanh \circ \left( p\tan ^{-1} \right) }\) which extends the main result of [3].
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Dedicated to Professor János Aczél on the occasion of his 90th birthday
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Kahlig, P., Matkowski, J. Second order iterative functional equations related to a competition equation. Aequat. Math. 89, 107–117 (2015). https://doi.org/10.1007/s00010-014-0307-1
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DOI: https://doi.org/10.1007/s00010-014-0307-1