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Some fixed point theorems

Part of: Nonlinear operators and their properties Connections with other structures, applications Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

P. V. Subrahmanyam  and
I. L. Reilly
P. V. Subrahmanyam
Affiliation:
Department of MathematicsIndian Institute of TechnologyMadras 600 036, India
I. L. Reilly
Affiliation:
Department of Mathematics and StatisticsUniversity of AucklandAuckland, New Zealand
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Abstract

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Banach's contraction principle guarantees the existence of a unique fixed point for any contractive selfmapping of a complete metric space. This paper considers generalizations of the completeness of the space and of the contractiveness of the mapping and shows that some recent extensions of Banach's theorem carry over to spaces whose topologies are generated by families of quasi-pseudometrics.

Keywords

contractionsequentially completequasi-gauge spacefixed point.

MSC classification

Secondary: 47H10: Fixed-point theorems 54H25: Fixed-point and coincidence theorems 54E40: Special maps on metric spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 3 , December 1992 , pp. 304 - 312
Copyright
Copyright © Australian Mathematical Society 1992

References

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