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On Certain Simultaneous Functional Equations

Published online by Cambridge University Press:  20 November 2018

T. D. Howroyd
T. D. Howroyd*
Affiliation:
University of New Brunswick, Fredericton, New Brunswick
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G. de Rham [1] has shown that certain remarkable curves, defined by limits of sequences of inscribed polygons, are solutions of functional equations of the form

If the functions FP (z) (p = 1,2) are contraction mappings of the complex plane into itself, i.e. for fixed r < 1

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 8 , Issue 1 , February 1965 , pp. 77 - 82
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. de Rham, G., Sur quelques courbes définies par des equations fonctionnelles, Univ. e Politec, Torino, Rend, Sem. Mat. 16 (1956-7), 101-113.Google Scholar
2. de Rham, G., Sur une courbe plane, Journal de Math, Pures et Appl., 35 (1956), 25-42.Google Scholar