Abstract
Let X be a real separable F-space. We characterize solutions \({f:X\to\mathbb{R}}\) and \({M:\mathbb{R}\to\mathbb{R}}\) of the equation f(x + M(f(x))y) = f(x)f(y) such that f is bounded on a nonzero Christensen measurable set. Our result generalizes [Jabłońska in Acta Math Hung 125(1–2):113–119 2009, Theorem 1].
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Jabłońska, E. Christensen measurability and some functional equation. Aequat. Math. 81, 155–165 (2011). https://doi.org/10.1007/s00010-010-0056-8
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DOI: https://doi.org/10.1007/s00010-010-0056-8