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On the uniqueness of solutions of the functional equation \(\varphi(x+f(x))=\varphi (x)+ \varphi (f(x))\). (English) Zbl 0249.39004


MSC:

39B05 General theory of functional equations and inequalities
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References:

[1] Aczél, J.,Lectures on Functional Equations and Their Applications (Academic Press, New York-London, 1966 [Math. in Science and Engineering, Vol. 19]). · Zbl 0139.09301
[2] Banach, S.,Sur l’équation fonctionnelle f (x + y) = f (x) + f (y), Fund. Math.1, 123–124 (1920). · JFM 47.0235.02
[3] Kuczma, M.,Functional Equations in a Single Variable (PWN, Warszawa, 1968 [Monografie Matematyczne, Vol. 46]). · Zbl 0196.16403
[4] Kuczma, M.,A Characterization of the Exponential and Logarithmic Functions by Functional Equations, Fund. Math.52, 283–288 (1963). · Zbl 0126.12304
[5] Sierpiński, W.,Sur l’équation fonctionnelle f (x + y) = f (x) + f (y), Fund. Math.1, 116–122 (1920). · JFM 47.0235.01
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