Summary
A new shorter proof is given for the Theorem of P. Volkmann and H. Weigel determining the continuous solutionsf:R → R of the Baxter functional equationf(f(x)y + f(y)x − xy) = f(x)f(y). The proof is based on the well known theorem of J. Aczél describing the continuous, associative, and cancellative binary operations on a real interval.
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References
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Brzdek, J. On the Baxter functional equation. Aeq. Math. 52, 105–111 (1996). https://doi.org/10.1007/BF01818329
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DOI: https://doi.org/10.1007/BF01818329