Abstract
In the paper Brillouët-Belluot and Ebanks (Aequationes Math 60:233–242, 2000), the authors found all continuous functions f: [0, 1] → [0, + ∞) which verify f(0) = f(1) = 0 and the functional equation
where c and d are given real numbers with c ≠ 0. In the present paper we obtain all continuous solutions \({f: \mathbb{R} \rightarrow \mathbb{R}}\) of the functional equation (1).
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Brillouët-Belluot, N. On a functional equation of Bruce Ebanks. Aequat. Math. 87, 173–189 (2014). https://doi.org/10.1007/s00010-013-0209-7
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DOI: https://doi.org/10.1007/s00010-013-0209-7