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dc.contributor.author | Mutangadura, Simba A.![]() |
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dc.date.accessioned | 2014-05-12T12:25:29Z | |
dc.date.available | 2014-05-12T12:25:29Z | |
dc.date.issued | 2014 | |
dc.description.abstract | Recall that Ishikawa’s theorem [4] provides an iterative procedure that yields a sequence which converges to a fixed point of a Lipschitz pseudocontrative map T : C ! C, where C is a compact convex subset of a Hilbert space X. The conditions on T and C, as well as the fact that X has to be a Hilbert space, are clearly very restrictive. Modifications of the Ishikawa’s iterative scheme have been suggested to take care of, for example, the case where C is no longer compact or where T is only continuous. The purpose of this paper is to explore those cases where the unmodified Ishikawa iterative procedure still yields a sequence that converges to a fixed point of T, with C no longer compact. We show that, if T has a fixed point, then every Ishikawa iteration sequence converges in norm to a fixed point of T if C is boundedly compact or if the set of fixed points of T is “suitably large”. In the process, we also prove a convexity result for the fixed points of continuous pseudocontractions. | en_US |
dc.description.embargo | 2015-03-30 | |
dc.description.librarian | hb2014 | en_US |
dc.description.uri | http://www.tandfonline.com/loi/tqma20 | en_US |
dc.identifier.citation | Mutangadura, SA 2014, 'Convergence of Ishikawa iterations on noncompact sets', Quaestiones Mathematicae, vol. 37, no. 2, pp. 191-198.. | en_US |
dc.identifier.issn | 0379-9468 (print) | |
dc.identifier.issn | 1727-933X (online) | |
dc.identifier.other | 10.2989/16073606.2013.779997 | en |
dc.identifier.uri | http://hdl.handle.net/2263/39773 | |
dc.language.iso | en | en_US |
dc.publisher | Taylor & Francis | en_US |
dc.rights | © 2014 Wiley. This is an electronic version of an article published in Quaestiones Mathematicae, vol. 37, no. 2, pp. 191-198, 2014. doi : 10.2989/16073606.2013.779997. Quaestiones Mathematicaeis available online at : http://www.tandfonline.com/loi/tqma20. | en_US |
dc.subject | Convergence | en_US |
dc.subject | Ishikawa iterative | en_US |
dc.subject | Fixed point | en_US |
dc.subject | Noncompact sets | en_US |
dc.title | Convergence of Ishikawa iterations on noncompact sets | en_US |
dc.type | Postprint Article | en_US |