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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| Format: | Article |
| Language: | English |
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Wiley
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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| _version_ | 1850237142770384896 |
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| author | Xue Zhiqun |
| author_facet | Xue Zhiqun |
| author_sort | Xue Zhiqun |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-01a0abfcd3454fff92a4063fa0dd54a4 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-01a0abfcd3454fff92a4063fa0dd54a42025-08-20T02:01:49ZengWileyInternational 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 |
| spellingShingle | Xue Zhiqun Iterative approximation of fixed point for Φ-hemicontractive mapping without Lipschitz assumption International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | 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 |
| url | http://dx.doi.org/10.1155/IJMMS.2005.2711 |
| work_keys_str_mv | AT xuezhiqun iterativeapproximationoffixedpointforphhemicontractivemappingwithoutlipschitzassumption |