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On a problem of Nicole Brillouët-Belluot

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Abstract

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 : I → I 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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Reference

  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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  1. Institute of Mathematics, University of Silesia, Bankowa 14, 40-007, Katowice, Poland

    Janusz Morawiec

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  1. Janusz Morawiec
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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). https://doi.org/10.1007/s00010-011-0096-8

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  • DOI: https://doi.org/10.1007/s00010-011-0096-8

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