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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
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