Abstract
Let X be a real linear space. We characterize solutions \({f, g : X \rightarrow \mathbb{R}}\) of the equation f(x + g(x)y) = f(x)f(y), where f is continuous on rays. Our result refers to papers by Brzdȩk (Acta Math Hungar 101:281–291, 2003), Chudziak (Aequat Math, doi:10.1007/s00010-013-0228-4, 2013) and Jabłońska (J Math Anal Appl 375:223–229, 2011).
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Jabłońska, E. On continuous on rays solutions of a composite-type equation. Aequat. Math. 89, 583–590 (2015). https://doi.org/10.1007/s00010-013-0243-5
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DOI: https://doi.org/10.1007/s00010-013-0243-5