dc.contributor.author |
Mutangadura, Simba A.
|
|
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 |