Complex iterated radicals
Abstract: We prove the convergence of the sequence defined by real, for any choice of . Let . If or has only one fixed point and converges to for any . If has the fixed points and , and for any converges to . If has the fixed points and and converges to if and to otherwise. We show that convergence is strictly monotone when the neighborhood system is the pencil of coaxial circles with and as limiting points, and give rates of convergence.
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Keywords: Iterated radicals, convergence, rate of convergence, coaxial circles
Article copyright: © Copyright 1973 American Mathematical Society