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Literatur
C. Ryll-Nardzewski, Sur les moyennes,Studia Mathematica,11 (1949), pp. 31–37.
B. Knaster, Sur une équivalence pour les fonctions,Colloquium Mathematicum,2 (1949), pp. 1–4.
J. Aczél, On mean values,Bull. Amer. Math. Soc.,54 (1948), pp. 392–400.
J. Aczél, К теории средних величин (under press).
A. R. Schweitzer, Remarks on functional equation,Bull. Amer. Math. Soc.,21 (1914), pp. 23–29.
This method of proof is due toJ. Aczél; see loc. cit.4 К теории средних величих (under press), esp. § 4.
J. Aczél has kindly called my attention to the fact that if we do not suppose the differentiability then there exist also more general solutions of (15). E. g. ifg(t)≡g╪±1 is constant, then also λ(x, y)=χ[log|x−y|] with an arbitrary periodic χ(t)=χ[t+log|g|] satisfies (15).
The problem of characterisation of these functions by a functional equation was raised byJ. Aczél in a lecture.
H. W. Pexider,Monatshefte für Math. u. Phys.,14 (1903), p. 293.
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Hosszú, M. On the functional equation of distributivity. Acta Mathematica Academiae Scientiarum Hungaricae 4, 159–167 (1953). https://doi.org/10.1007/BF02020361
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DOI: https://doi.org/10.1007/BF02020361