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A fixed point theorem for non-expansive, condensing mappings
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
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- Research Article
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- Copyright © Australian Mathematical Society 1980
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