期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1991
卷号：14
DOI：10.1155/S0161171291000236
出版社：Hindawi Publishing Corporation
摘要：A basic theorem of iteration theory (Henrici [6]) states that f analytic on
the interior of the closed unit disk D and continuous on D with Int(D)f(D) carries
any point z ϵ D to the unique fixed point α ϵ D of f. That is to say, fn(z)→α as
n→∞. In [3] and [5] the author generalized this result in the following way:
Let Fn(z):=f1∘…∘fn(z). Then fn→f uniformly on D implies Fn(z)λ, a
constant, for all z ϵ D. This kind of compositional structure is a generalization of
a limit periodic continued fraction. This paper focuses on the convergence behavior
of more general inner compositional structures f1∘…∘fn(z) where the fj's are
analytic on Int(D) and continuous on D with Int(D)fj(D), but essentially random.
Applications include analytic functions defined by this process.
