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On the construction of convergent iterative sequences of polynomials

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Qiu Weiyuan
Qiu Weiyuan
Affiliation:
Institute of Mathematics Fudan UniversityShangai People's Republic of, China
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Abstract

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We answer two conjectures suggested by Zalman Rubinstein. We prove his Conjecture 1, that is, we construct convergent iterative sequences for with an arbitrary initial point, where with m ≥ 2. We also show by several counterexamples that Rubinstein's Conjecture 2 is generally false.

MSC classification

Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 3 , December 1989 , pp. 382 - 390
Copyright
Copyright © Australian Mathematical Society 1989

References

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