A direct proof of a theorem of K. Baron
In his work on the Gołąb-Schinzel equation, K. Baron shows a theorem concerning continuous complex-valued solutions, defined on the
complex plane. In this note, we will give a direct proof of this theorem, which does not use the form of the general solution of the Gołąb-Schinzel equation.
2. K. Baron, On the continuous solutions of the Gołąb-Schinzel equation, Aequationes Math. 38 (1989), 155-162.
3. N. Bourbaki, General Topology, Part 2, Addison-Wesley, Reading, Ma., 1966.
4. P. Javor, On the general solution of the functional equation f(x + yf(x)) = 3Df(x)f(y), Aequationes Math. 1 (1968), 235-238.
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