XXIV.—The Solution of a Functional Equation
1952 ◽
Vol 63
(4)
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pp. 336-345
Keyword(s):
SynopsisAnalytic 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.
2009 ◽
Vol 2009
◽
pp. 1-14
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2014 ◽
Vol 81
(4)
◽
pp. 455-482
◽
Keyword(s):