On the Baxter functional equation
Copyright policy )On the Baxter functional equation
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.
- DigiZeitschriften Germany
- Pedagogical University Mozambique
510.mathematics, Functional equations for real functions, continuous cancellative abelian semigroups, Baxter functional equation, continuous real solutions, Article
510.mathematics, Functional equations for real functions, continuous cancellative abelian semigroups, Baxter functional equation, continuous real solutions, Article
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