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Necessary and sufficient fixed point critera involving attractors

Published online by Cambridge University Press:  17 April 2009

Jacek Jachymski
Jacek Jachymski
Affiliation:
Institute of Mathematics Technical University, of Lódź ul. Zwirki 36 90–924 Lódź, Poland
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Let f be a continuous self-map on a complete metric space X and p ∈ X. Let c be a positive real. Equivalent conditions are given for the singleton {p} to be an attractor of a set of c−fixed points of f. We also establish equivalent conditions for the existence of a contractive fixed point of f. These results subsume a body of fixed point theorems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 109 - 116
Copyright
Copyright © Australian Mathematical Society 1993

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