The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence
Charles proved the convergence of Picard-type iteration for generalized Φ−accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ−quasi-accretive mappings and fixed points of strongly Φ−hemi-contractions, we extend the results to Noor iter...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/9064369 |
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| author | Linxin Li Dingping Wu |
| author_facet | Linxin Li Dingping Wu |
| author_sort | Linxin Li |
| collection | DOAJ |
| description | Charles proved the convergence of Picard-type iteration for generalized Φ−accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ−quasi-accretive mappings and fixed points of strongly Φ−hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized Φ−hemi-contractive mappings. Finally, we analyze the rate of convergence of four iterative schemes, namely, Noor iteration, iteration of Corollary 2, SP iteration, and iteration of Corollary 4. |
| format | Article |
| id | doaj-art-ff8def1b097b407a8f10661f3c2d4821 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-ff8def1b097b407a8f10661f3c2d48212025-02-03T07:23:54ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/90643699064369The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of ConvergenceLinxin Li0Dingping Wu1Department of Mathematics, Chengdu University of Information Technology, Chengdu 610225, ChinaDepartment of Mathematics, Chengdu University of Information Technology, Chengdu 610225, ChinaCharles proved the convergence of Picard-type iteration for generalized Φ−accretive nonself-mappings in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ−quasi-accretive mappings and fixed points of strongly Φ−hemi-contractions, we extend the results to Noor iterative process and SP iterative process for generalized Φ−hemi-contractive mappings. Finally, we analyze the rate of convergence of four iterative schemes, namely, Noor iteration, iteration of Corollary 2, SP iteration, and iteration of Corollary 4.http://dx.doi.org/10.1155/2021/9064369 |
| spellingShingle | Linxin Li Dingping Wu The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence Journal of Mathematics |
| title | The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence |
| title_full | The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence |
| title_fullStr | The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence |
| title_full_unstemmed | The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence |
| title_short | The Convergence of Three-Step Iterative Schemes for Generalized Φ−Hemi-Contractive Mappings and the Comparison of Their Rate of Convergence |
| title_sort | convergence of three step iterative schemes for generalized φ hemi contractive mappings and the comparison of their rate of convergence |
| url | http://dx.doi.org/10.1155/2021/9064369 |
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