Abstract
We study the functional equation f(x)f −1(x) = x 2 imposing no continuity assumptions on its bijective solutions defined on an interval. All the continuous bijections satisfying the equation were determined by the second author in (Aequat. Math. (in print), 2011) when solving the problem (Problem posed during the forty-ninth International Symposium on Functional Equations 2011) posed by Brillouët-Belluot.
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Brillouët-Belluot N.: Problem posed during the Forty-nine International Symposium on Functional Equations. Graz-Mariatrost, Austria (2011)
Morawiec, J.: On a problem of Nicole Brillouët-Belluot. Aequat. Math. doi:10.1007/s00010-011-0096-8 (2011)
Acknowledgements
The second author was supported by Silesian University Mathematics Department (Iterative Functional Equations and Real Analysis program).
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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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Jarczyk, W., Morawiec, J. Note on an equation occurring in a problem of Nicole Brillouët-Belluot. Aequat. Math. 84, 227–233 (2012). https://doi.org/10.1007/s00010-011-0097-7
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DOI: https://doi.org/10.1007/s00010-011-0097-7