Fixed Point Theorems on Closed Sets Through Abstract Cones
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 | **Please note that the full text is embargoed** 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 |