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Diametrically contractive mappings

Published online by Cambridge University Press:  17 April 2009

Hong-Kun Xu
Hong-Kun Xu
Affiliation:
School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, Private Bag X54001, Durban 4000, South Africa, e-mail: xuhk@ukzn.ac.za
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A contractive mapping on a complete metric space may fail to have a fixed point. Diametrically contractive mappings are introduced and it is shown that a diametrically contractive self-mapping of a weakly compact subset of a Banach space always has a fixed point.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 463 - 468
Copyright
Copyright © Australian Mathematical Society 2004

References

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