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XXIV.—The Solution of a Functional Equation*

Published online by Cambridge University Press:  14 February 2012

A. H. Read
A. H. Read
Affiliation:
United College, University of St Andrews.
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Synopsis

Analytic solutions of the functional equation f[z, φ{g(z)}] = φ(z), in which f(z, w) and g(z) are given analytic functions and φ(z) is the unknown function, are investigated in the neighbourhood of points ζ such that g(ζ) = ζ. Conditions are established under which each solution φ(z) may be given as the limit of a sequence of functions φn(z), defined by the recurrence relation φn+1(Z) = ƒ[z, φn{g(z)}], the function φn(z) being to a large extent arbitrary.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 63 , Issue 4 , 1952 , pp. 336 - 345
Copyright
Copyright © Royal Society of Edinburgh 1952

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References

REFERENCES TO LITERATURE

Fatou, P., 1920. “Sur les Équations Fonctionnelles”, Bull. Soc. Math. France, XLVIII, 261.Google Scholar
Koenigs, G., 1884. “Recherches sur les Équations Fonctionnelles”, Ann. Sci. Éc. Norm. Sup. Paris, ser. 3, 1, supplement, 19.Google Scholar
Montel, P., 1927. Leçons sur les Familles Normales de Fonctions Analytiques, Paris.Google Scholar