On the Baxter functional equation (Q1924293)
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scientific article; zbMATH DE number 935130
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Baxter functional equation |
scientific article; zbMATH DE number 935130 |
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On the Baxter functional equation (English)
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14 October 1996
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The author offers a shorter way of finding all continuous real solutions of the functional equation [cf. \textit{P. Volkmann} and \textit{H. Weigel}, ibid. 27, 135-149 (1984; Zbl 0544.39006)] \(f[f(x)y + f(y)x-xy] = f(x)f(y)\) (all but one type turn out to be piecewise linear). The proof is based on the result that all continuous cancellative abelian semigroups on real intervals are continuously isomorphic to infinite intervals under ordinary addition.
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Baxter functional equation
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continuous real solutions
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continuous cancellative abelian semigroups
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