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Fixed Point Theorems on Closed Sets Through Abstract Cones

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Fixed Point Theorems on Closed Sets Through Abstract Cones

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dc.contributor.author Lakshmikantham, V. en
dc.contributor.author Eisenfeld, Jerome en
dc.date.accessioned 2010-06-14T14:11:21Z en
dc.date.available 2010-06-14T14:11:21Z en
dc.date.issued 1976-03 en
dc.identifier.uri http://hdl.handle.net/10106/2492 en
dc.description.abstract Let D be a closed subset of a complete metric space (X,p). We seek (i) conditions upon which a map T : D -> X has a fixed point in D and (ii) the construction of an iterative sequence whose limit is a fixed point in D. If X is a Banach space then a classical approach is to set G = I - T and use a numerical search method to minimize ||GX|| in D. Another approach, which does not require a Banach space structure, was recently introduced by Caristi and Kirk ([1],[2]). They prove that a metrically inward contractor map T has a fixed point. Both methods assume conditions which guarantee that for arbitrary x in D there exists y in D such that p(y,Ty) < p(x,TX). This condition is the basis of our study. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;39 en
dc.subject Fixed point en
dc.subject Closed systems en
dc.subject Generalized norm en
dc.subject Abstract cones en
dc.subject Fixed point theorem en
dc.subject Closed sets en
dc.subject Abstract cone en
dc.subject.lcsh Mathematics Research en
dc.subject.lcsh Mathematics Research en
dc.title Fixed Point Theorems on Closed Sets Through Abstract Cones en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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