Convergence of Ishikawa iterations on noncompact sets

Show simple item record Mutangadura, Simba A. 2014-05-12T12:25:29Z 2014-05-12T12:25:29Z 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 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.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 : 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

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