Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption
Let E be an arbitrary real Banach space and let K be a nonempty closed convex subset of E such that K+K⊂K. Assume that T:K→K is a uniformly continuous and Φ-hemicontractive mapping. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique fixed point of T.
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| Language: | English |
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Hindawi Limited
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.2711 |
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doaj-01a0abfcd3454fff92a4063fa0dd54a42020-11-24T22:55:02ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005172711271810.1155/IJMMS.2005.2711Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumptionXue Zhiqun0Department of Mathematics, Shijiazhuang Railway College, Shijiazhuang 050043, ChinaLet E be an arbitrary real Banach space and let K be a nonempty closed convex subset of E such that K+K⊂K. Assume that T:K→K is a uniformly continuous and Φ-hemicontractive mapping. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique fixed point of T.http://dx.doi.org/10.1155/IJMMS.2005.2711 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Xue Zhiqun |
| spellingShingle |
Xue Zhiqun Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Xue Zhiqun |
| author_sort |
Xue Zhiqun |
| title |
Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption |
| title_short |
Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption |
| title_full |
Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption |
| title_fullStr |
Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption |
| title_full_unstemmed |
Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption |
| title_sort |
iterative approximation of fixed point for φ-hemicontractive mapping without lipschitz assumption |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2005-01-01 |
| description |
Let E be an arbitrary real Banach space and let K be a nonempty closed convex subset of E such that K+K⊂K. Assume that T:K→K is a uniformly continuous and Φ-hemicontractive mapping. It is shown that the Ishikawa iterative sequence with errors converges strongly to the unique fixed point of T. |
| url |
http://dx.doi.org/10.1155/IJMMS.2005.2711 |
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AT xuezhiqun iterativeapproximationoffixedpointforphhemicontractivemappingwithoutlipschitzassumption |
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1725658318155808768 |