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Sets of Convergence for Series Defined by Iteration1

Published online by Cambridge University Press:  20 November 2018

George Brauer
George Brauer*
Affiliation:
University of Minnesota
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Let f(x) be a real-valued function defined on an interval Ia: [ 0, a ]. For each point x in Ia we form the series , where u0 and un+1 = f(un) for n ≥ 0. If the series converges, x will be called a point of convergence; if this series diverges, x will be called a point of divergence. La this note several properties of sets of convergence2 will be obtained.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 9 , Issue 1 , April 1966 , pp. 83 - 87
Copyright
Copyright © Canadian Mathematical Society 1966

Footnotes

1

This research was supported by NSFG 24295.

References

1. Fort, M.K. Jr.andSeymour, Schuster, Convergence of series whose terms are defined recursively, Amer. Math. Monthly, 71 (1964), 994-998.Google Scholar