On the boundedness of the associated sequence of Mann iteration for several operator classes with applications
We prove that the associated sequence of Mann iteration is decreasing and hence bounded provided that the operator satisfies minimal assumptions. In particular we obtain for a nonexpansive operator that the associated sequence of Ishikawa iteration is decreasing for a nonexpansive operator. Applicat...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2005-08-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/808 |
| _version_ | 1818109432087707648 |
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| author | Ştefan M. Şoltuz |
| author_facet | Ştefan M. Şoltuz |
| author_sort | Ştefan M. Şoltuz |
| collection | DOAJ |
| description | We prove that the associated sequence of Mann iteration is decreasing and hence bounded provided that the operator satisfies minimal assumptions. In particular we obtain for a nonexpansive operator that the associated sequence of Ishikawa iteration is decreasing for a nonexpansive operator. Applications to the convergence of Mann iteration are given. |
| first_indexed | 2024-12-11T02:31:09Z |
| format | Article |
| id | doaj.art-cf96b99c89e54003aa7de2a9fd9742f8 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-12-11T02:31:09Z |
| publishDate | 2005-08-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-cf96b99c89e54003aa7de2a9fd9742f82022-12-22T01:23:50ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2005-08-01342On the boundedness of the associated sequence of Mann iteration for several operator classes with applicationsŞtefan M. Şoltuz0Tiberiu Popoviciu, Institute of Numerical Analysis, Romanian AcademyWe prove that the associated sequence of Mann iteration is decreasing and hence bounded provided that the operator satisfies minimal assumptions. In particular we obtain for a nonexpansive operator that the associated sequence of Ishikawa iteration is decreasing for a nonexpansive operator. Applications to the convergence of Mann iteration are given.https://ictp.acad.ro/jnaat/journal/article/view/808Ishikawa-Mann iterationassociated Mann sequence |
| spellingShingle | Ştefan M. Şoltuz On the boundedness of the associated sequence of Mann iteration for several operator classes with applications Journal of Numerical Analysis and Approximation Theory Ishikawa-Mann iteration associated Mann sequence |
| title | On the boundedness of the associated sequence of Mann iteration for several operator classes with applications |
| title_full | On the boundedness of the associated sequence of Mann iteration for several operator classes with applications |
| title_fullStr | On the boundedness of the associated sequence of Mann iteration for several operator classes with applications |
| title_full_unstemmed | On the boundedness of the associated sequence of Mann iteration for several operator classes with applications |
| title_short | On the boundedness of the associated sequence of Mann iteration for several operator classes with applications |
| title_sort | on the boundedness of the associated sequence of mann iteration for several operator classes with applications |
| topic | Ishikawa-Mann iteration associated Mann sequence |
| url | https://ictp.acad.ro/jnaat/journal/article/view/808 |
| work_keys_str_mv | AT stefanmsoltuz ontheboundednessoftheassociatedsequenceofmanniterationforseveraloperatorclasseswithapplications |