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Fixed points and iteration homotopies

Published online by Cambridge University Press:  09 April 2009

Francis J. Papp
Francis J. Papp
Affiliation:
Department of Mathematics University of LethbridgeLethbridge, Alberta, Canada
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Suppose that Ф is a topological space equipped with a Hausdorff topology and that T is a continuous function mapping Ф into Ф. We discuss the existence and uniqueness of fixed points of T and the convergence of the Picard sequence of iterates, from the viewpoint of the existence of a homotopy with special properties.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 17 - 20
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Chu, S. C. and Diaz, J. B., ‘A Fixed Point Theorem for ‘In the Large’ Application of the Contraction Principle’, Atti della Accademia delle Scienze di Torino, Vol. XCIX, (1964–1965), 351–363.Google Scholar
[2]Hewitt, E. and Stromberg, K., Real and Abstract Analysis (New York: Springer-Verlag; 1965).Google Scholar