Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings
A new class of α-hemicontractive maps T for which the strong convergence of the Ishikawa iteration algorithm to a fixed point of T is assured is introduced and studied. The study is a continuation of a recent study of a new class of α-demicontractive mappings T by L. Mărușter and Ș. Mărușter, Mathem...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2015-07-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/awutm-2015-0008 |
| _version_ | 1818469189993627648 |
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| author | Osilike Micah Okwuchukwu Onah Anthony Chibuike |
| author_facet | Osilike Micah Okwuchukwu Onah Anthony Chibuike |
| author_sort | Osilike Micah Okwuchukwu |
| collection | DOAJ |
| description | A new class of α-hemicontractive maps T for which the strong convergence of the Ishikawa iteration algorithm to a fixed point of T is assured is introduced and studied. The study is a continuation of a recent study of a new class of α-demicontractive mappings T by L. Mărușter and Ș. Mărușter, Mathematical and Computer Modeling 54 (2011) 2486-2492 in which they proved strong convergence of the Mann iteration scheme to a fixed point of T. Our class of α-hemicontractive maps is more general than the class of α-demicontractive maps. No compactness assumption is imposed on the operator or it’s domain, and no additional requirement is imposed on the set of fixed points. |
| first_indexed | 2024-04-13T21:21:14Z |
| format | Article |
| id | doaj.art-c0ce0fdfb90741cfb5126a08fdc5998b |
| institution | Directory Open Access Journal |
| issn | 1841-3307 |
| language | English |
| last_indexed | 2024-04-13T21:21:14Z |
| publishDate | 2015-07-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annals of the West University of Timisoara: Mathematics and Computer Science |
| spelling | doaj.art-c0ce0fdfb90741cfb5126a08fdc5998b2022-12-22T02:29:29ZengSciendoAnnals of the West University of Timisoara: Mathematics and Computer Science1841-33072015-07-0153115116110.1515/awutm-2015-0008awutm-2015-0008Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappingsOsilike Micah Okwuchukwu0Onah Anthony Chibuike1Department of Mathematics, University of Nigeria, Nsukka, NigeriaDepartment of Mathematics, University of Nigeria, Nsukka, NigeriaA new class of α-hemicontractive maps T for which the strong convergence of the Ishikawa iteration algorithm to a fixed point of T is assured is introduced and studied. The study is a continuation of a recent study of a new class of α-demicontractive mappings T by L. Mărușter and Ș. Mărușter, Mathematical and Computer Modeling 54 (2011) 2486-2492 in which they proved strong convergence of the Mann iteration scheme to a fixed point of T. Our class of α-hemicontractive maps is more general than the class of α-demicontractive maps. No compactness assumption is imposed on the operator or it’s domain, and no additional requirement is imposed on the set of fixed points.https://doi.org/10.1515/awutm-2015-0008α-demicontractive mapsα-hemicontractive mapsfixed pointsishikawa iterationstrong convergence |
| spellingShingle | Osilike Micah Okwuchukwu Onah Anthony Chibuike Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings Annals of the West University of Timisoara: Mathematics and Computer Science α-demicontractive maps α-hemicontractive maps fixed points ishikawa iteration strong convergence |
| title | Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings |
| title_full | Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings |
| title_fullStr | Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings |
| title_full_unstemmed | Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings |
| title_short | Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings |
| title_sort | strong convergence of the ishikawa iteration for lipschitz α hemicontractive mappings |
| topic | α-demicontractive maps α-hemicontractive maps fixed points ishikawa iteration strong convergence |
| url | https://doi.org/10.1515/awutm-2015-0008 |
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