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Partial difference equations analogous to the Cauchy-Riemann equations and related functional equations on rings and fields. (English) Zbl 0830.39015

Let \(S\) be a set endowed with two binary operations \((*)\) and \((\cdot)\) and \(G(+)\) be an Abelian group. The authors solve the functional equation \(f(x*t,y) + g(x,y \cdot t) = h(x,y)\), for \(x,y,t \in S\), where \(f,g,h : S \times S \to G\).

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
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References:

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