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Variational Aspects of the Abel and Schroder Functional Equations
Published online by Cambridge University Press: 20 November 2018
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Given an analytic function f, the successive iterates of f are defined by
f[0](z) = z, f[n+1](z) = f{f[n](z)} for every z.
In particular f[1](z) = {f[0](z)} f(z). Extensive study has been given [1] to the problem of generalizing the iterates f[n], for integer n, to f[t] for arbitrary t, where the iterative character of f[t] is to be preserved by the conditions,
f[0](z) = z and f[s]{f[t](z)} = f[s+t](z) for arbitrary s and t.
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- Copyright © Canadian Mathematical Society 1963
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