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Fixed Point Theorems for Expanding Maps

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Fixed Point Theorems for Expanding Maps

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dc.contributor.author Williams, B. B. en
dc.contributor.author Gillespie, A. A. en
dc.date.accessioned 2010-06-09T14:29:53Z en
dc.date.available 2010-06-09T14:29:53Z en
dc.date.issued 1981-03 en
dc.identifier.uri http://hdl.handle.net/10106/2412 en
dc.description.abstract Suppose (X,d) is a metric space, h > 0 and T: X -> X. We shall use the notation T E E(h) to mean [see pdf for notation] for each x,y E X. If h > 1, then T will be called an expanding map. Clearly T E E(h) implies T is a 1-1 function and [see pdf for notation] for each x,y E T(X). In this paper some conditions are found to insure that an expanding map will have a fixed point. It is shown that each finite dimensional Banach space X has the following property: each continuous and expanding map from X into X has a fixed point. It is also shown that not all infinite dimensional Banach spaces have the above property. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;154 en
dc.subject Banach spaces en
dc.subject Fixed point theorem en
dc.subject Expanding map en
dc.subject.lcsh Mathematics Research en
dc.title Fixed Point Theorems for Expanding Maps en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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