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Convergence of iterates and differentiability

Published online by Cambridge University Press:  09 April 2009

Francis J. Papp  and
Robert M. Nielsen
Francis J. Papp
Affiliation:
Department of Mathematics, University of LethbridgeAlberta TIK 3M4, Canada
Robert M. Nielsen
Affiliation:
Department of Mathematics, University of LethbridgeAlberta TIK 3M4, Canada
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Given a function T mapping a Hausdorff locally convex topological vector space Φ into Φ and a point φ0 of Φ, convergence of the elementary filter associated with the sequence of iterates determined by T and φ0 is investigated. Sufficient conditions that the limit φ if it exists, be a fixed point of T are given and in the case Φ is the space of real valued functions of a real variable differentiability of the limit function φ is investigated.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 3 , November 1972 , pp. 269 - 273
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Brace, J. W., ‘Convergence on Filters and Simple Equicontinuity’, Ill. J. Math., IX, 1965, 286–296.Google Scholar
[2]Nielsen, R. M., ‘Completion in the Bidual’, J. Australian Math. Soc., VIII (2) 1968, 238–241.CrossRefGoogle Scholar
[3]Nielsen, R. M., ‘Pointwise Convergence and Differentiability’, J. Math. Anal. and Appl., XXV 1969, 337–340.CrossRefGoogle Scholar