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On Darboux solutions of the Euler's equation

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Summary

We construct a non-constant Darboux functionf: R → R which is a solution of the Euler's functional equationf(x + f(x)) = f(x) for everyx. This function is a counter-example to a statement given in the literature.

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References

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Authors and Affiliations

  1. Department of Mathematics, Komensky University, ČSR-842-15, Bratislava, Czechoslovakia

    J. Smítal

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  1. J. Smítal
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Smítal, J. On Darboux solutions of the Euler's equation. Aeq. Math. 37, 279–281 (1989). https://doi.org/10.1007/BF01836450

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  • DOI: https://doi.org/10.1007/BF01836450

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