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Cauchy differences that depend on the product of arguments. (English) Zbl 0780.39007
From the authors’ abstract: All functions $$f$$, defined on a field $$K$$ and taking values in a uniquely 2-divisible group $$G$$, are determined for which the Cauchy difference $$f(x+y)-f(x)-f(y)$$ depends only on the product $$xy$$ for all $$x$$, $$y\in K$$. Using this result the general solution of the functional equation $$f(x+y-\alpha xy)=h(x)+k(y)$$ is determined, where $$\alpha$$ is a fixed parameter in $$K$$. A special case of this equation is the Hosszu functional equation.
Reviewer: J.Schwaiger (Graz)

MSC:
 39B22 Functional equations for real functions