Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings
Our aim in this paper is to illustrate that the proof of main theorem of Rhoades and Şoltuz (2003) concerning the equivalence between the convergences of Ishikawa and Mann iterations for uniformly L-Lipschitzian asymptotically pseudocontractive maps is incorrect and to provide its correct version.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/274931 |
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| _version_ | 1832548127855345664 |
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| author | Haizhen Sun Zhiqun Xue |
| author_facet | Haizhen Sun Zhiqun Xue |
| author_sort | Haizhen Sun |
| collection | DOAJ |
| description | Our aim in this paper is to illustrate that the proof of main theorem of Rhoades and Şoltuz (2003) concerning the equivalence between the convergences of Ishikawa and Mann iterations for uniformly L-Lipschitzian asymptotically pseudocontractive maps is incorrect and to provide its correct version. |
| format | Article |
| id | doaj-art-7de95383c54d408db4f4557c01d63f03 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-7de95383c54d408db4f4557c01d63f032025-02-03T06:42:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/274931274931Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive MappingsHaizhen Sun0Zhiqun Xue1Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaDepartment of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, ChinaOur aim in this paper is to illustrate that the proof of main theorem of Rhoades and Şoltuz (2003) concerning the equivalence between the convergences of Ishikawa and Mann iterations for uniformly L-Lipschitzian asymptotically pseudocontractive maps is incorrect and to provide its correct version.http://dx.doi.org/10.1155/2013/274931 |
| spellingShingle | Haizhen Sun Zhiqun Xue Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings Journal of Applied Mathematics |
| title | Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings |
| title_full | Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings |
| title_fullStr | Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings |
| title_full_unstemmed | Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings |
| title_short | Reconsiderations on the Equivalence of Convergence between Mann and Ishikawa Iterations for Asymptotically Pseudocontractive Mappings |
| title_sort | reconsiderations on the equivalence of convergence between mann and ishikawa iterations for asymptotically pseudocontractive mappings |
| url | http://dx.doi.org/10.1155/2013/274931 |
| work_keys_str_mv | AT haizhensun reconsiderationsontheequivalenceofconvergencebetweenmannandishikawaiterationsforasymptoticallypseudocontractivemappings AT zhiqunxue reconsiderationsontheequivalenceofconvergencebetweenmannandishikawaiterationsforasymptoticallypseudocontractivemappings |