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The Christensen measurable solutions of a generalization of the Gołąb-Schinzel functional equation. (English) Zbl 0860.39034
The main result in the paper is the following. Let \(X\) be a linear separable \(F\)-space over the set of real (or complex) numbers. If the real (or complex) valued function \(f\) satisfies \(f(x+f (x)^ny) = f(x)f(y)\) for all \(x,y \in X\) then \(f\) is either continuous or the set of points where \(f(x)\) is not zero is a Christensen zero set. All continuous solutions are determined.

MSC:
39B52 Functional equations for functions with more general domains and/or ranges
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