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On a problem of Nicole Brillouët-Belluot

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We solve the problem posed by Nicole Brillouët-Belluot (During the Forty-ninth International Symposium on Functional Equations, 2011) of determining all continuous bijections f : II satisfying

$$f(x)f^{-1}(x) = x^2 \quad{\rm for\, every}\, x \in I,$$

where I is an arbitrary subinterval of the real line.

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  1. Brillouët-Belluot, N.: Problem posed during the Forty-nine International Symposium on Functional Equations, Graz-Mariatrost, Austria, 19–26 June 2011

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Correspondence to Janusz Morawiec.

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Morawiec, J. On a problem of Nicole Brillouët-Belluot. Aequat. Math. 84, 219–225 (2012).

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