Summary
In this paper theorems of P. Javor and N. Brillouët-J. Dhombres will be completed and a theorem of S. Wołodźko generalized, by describing complex-valued continuous solutions defined on a complex topological vector space of the Gołąb-Schinzel equation
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References
Aczél, J.,Lectures on functional equations and their applications. Academic Press, New York–London, 1966.
Bourbaki, N.,Eléments de mathématique. Livre III: Topologie générale. Herman, Paris, 1963.
Brillouet, N. andDhombres, J.,Equations fonctionelles et recherche de sous-groupes. Aequationes Math.31 (1986), 253–293.
Ilse, D., Lechmann, I. andSchulz, W.,Gruppoide und Funktionalgleichungen. VEB Deutscher Verlag der Wissenschaften, Berlin, 1984.
Javor, P.,On the general solution of the functional equation f(x + yf(x)) = f(x)f(y). Aequationes Math.1 (1968), 235–238.
Javor, P.,Continuous solutions of the functional equation f(x + yf(x)) = f(x)f(y). Proc. Internat. Sympos. on Toplogy and its Applications (Herceg-Novi, 1968). Savez Društava Mat. Fiz. i Astronom., Belgrade, 1969, pp. 206–209.
Plaumann, P. andStrambach, K.,Zweidimensionale Quasialgebren mit Nullteilern. Aequationes Math.15 (1977), 249–264.
Rudin, W.,Functional analysis. McGraw-Hill, New York, 1973.
Wołodźko, S.,Solution générale de l'équation fonctionelle f[x + yf(x)] = f(x)f(y). Aequationes Math.2 (1968), 12–29.
Wołodźko, S.,O ciaąglych rowiązaniach równania funkcyjnego f[x + yf(x)] = f(x)f(y) w zespolonej przestrzeni linowej unormowanej. Wyź. Szkoł. Ped. Krakow. Rocznik Nauk.-Dydakt. Zeszyt 41. Prace Mat.6 (1970), 199–204.
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Baron, K. On the continuous solutions of the Gołąb-Schinzel equation. Aeq. Math. 38, 155–162 (1989). https://doi.org/10.1007/BF01840001
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DOI: https://doi.org/10.1007/BF01840001