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A fixed point theorem for non-expansive, condensing mappings

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  09 April 2009

Eric Chandler  and
Gary Faulkner
Eric Chandler
Affiliation:
Department of Mathematics North Carolina State UniversityRaleigh, North Carolina 27650, U.S.A.
Gary Faulkner
Affiliation:
Department of Mathematics North Carolina State UniversityRaleigh, North Carolina 27650, U.S.A.
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Abstract

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A lemma is obtained which guarantees that non-expansive mappings on contractive spaces have fixed points. An example shows that Schauders's fixed point theorem cannot be extended to contractive spaces, but a theorem for contractive spaces, analogous to a result of B. N. Sadovskii on convex spaces, is derived from the lemma. Finally, some local results for ε-chainable contractive spaces are given.

Keywords

Fixed pointsnon-expansive mappingscondensing mappingscon-tractive metric spaces.

MSC classification

Secondary: 47H10: Fixed-point theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 4 , June 1980 , pp. 393 - 398
Copyright
Copyright © Australian Mathematical Society 1980

References

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