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XXIV.—The Solution of a Functional Equation*
Published online by Cambridge University Press: 14 February 2012
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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