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On the solutions of the functional equation \(f(xf(y)^ l + yf(x)^ k) = tf(x)f(y)\). (English) Zbl 0741.39008

Using some elementary but elegant methods the author proves that the only continuous solutions \(f:\mathbb{R}\to\mathbb{R}\) of the equation in title are constants \(f=0\) and \(f=1/t\). The same is true if \(f:X\to\mathbb{R}\) where \(X\) is a real linear space and \(f\) is continuous along rays.

MSC:

39B22 Functional equations for real functions
39B52 Functional equations for functions with more general domains and/or ranges
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