J Austral Math Soc Ser A 47 pp382--390, 1989.

On the Construction of Convergent Iterative Sequences of Polynomials

Qiu Weiyuan

(Received 24 December 1987; revised 11 July 1988)

Abstract

We answer two conjectures suggested by Zalman Rubinstein. We prove his Conjecture 1, that is, we construct convergent iterative sequences for f_m^-1(z) with an arbitrary initial point, where f_m(z) = z + z^m with m ł 2. We also show by several counterexamples that Rubinstein's Conjecture is generally false.

1980 AMS Subject Classification (1985 Revision): 30D05

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Authors

Qiu Weiyuan: Institute of Mathematics, Fudan University, Shanghai, People's Republic of China.

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Last Modified: Wed Feb 19 10:27:50 2003