A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spaces
In this paper, we introduce and study a new iterative algorithm which is a combination of a modified Mann iterative scheme and a generalized explicit methods (GEM) for finding a common fixed points of an infinite family of quasi-nonexpansive mappings in Banach spaces. Under suitable conditions, so...
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| Format: | Article |
| Language: | English |
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ATNAA
2019-06-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/742424 |
| _version_ | 1797917937753915392 |
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| author | Thierno M.M. Sow |
| author_facet | Thierno M.M. Sow |
| author_sort | Thierno M.M. Sow |
| collection | DOAJ |
| description | In this paper, we introduce and study a new iterative algorithm which is a combination of a modified
Mann iterative scheme and a generalized explicit methods (GEM) for finding a common fixed points of an
infinite family of quasi-nonexpansive mappings in Banach spaces. Under suitable conditions, some strong
convergence theorems for finding a common fixed points of an infinite family of quasi-nonexpansive mappings
are obtained without imposing any compactness assumption. Presented results improve and generalize many
known results in the current literature. |
| first_indexed | 2024-04-10T13:22:37Z |
| format | Article |
| id | doaj.art-88e9cdcface5483196891cc45768de97 |
| institution | Directory Open Access Journal |
| issn | 2587-2648 2587-2648 |
| language | English |
| last_indexed | 2024-04-10T13:22:37Z |
| publishDate | 2019-06-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-88e9cdcface5483196891cc45768de972023-02-15T16:12:00ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482587-26482019-06-01329010110.31197/atnaa.557149A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spacesThierno M.M. Sow0aDepartment of Mathematics, Gaston Berger University, Saint-Louis Senegal.In this paper, we introduce and study a new iterative algorithm which is a combination of a modified Mann iterative scheme and a generalized explicit methods (GEM) for finding a common fixed points of an infinite family of quasi-nonexpansive mappings in Banach spaces. Under suitable conditions, some strong convergence theorems for finding a common fixed points of an infinite family of quasi-nonexpansive mappings are obtained without imposing any compactness assumption. Presented results improve and generalize many known results in the current literature.https://dergipark.org.tr/en/download/article-file/742424common fixed points; quasi-nonexpansive mappings; midpoint rule; banach spaces. |
| spellingShingle | Thierno M.M. Sow A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spaces Advances in the Theory of Nonlinear Analysis and its Applications common fixed points; quasi-nonexpansive mappings; midpoint rule; banach spaces. |
| title | A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spaces |
| title_full | A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spaces |
| title_fullStr | A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spaces |
| title_full_unstemmed | A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spaces |
| title_short | A modified Mann iterative scheme based on the generalized explicit methods for quasi-nonexpansive mappings in Banach spaces |
| title_sort | modified mann iterative scheme based on the generalized explicit methods for quasi nonexpansive mappings in banach spaces |
| topic | common fixed points; quasi-nonexpansive mappings; midpoint rule; banach spaces. |
| url | https://dergipark.org.tr/en/download/article-file/742424 |
| work_keys_str_mv | AT thiernommsow amodifiedmanniterativeschemebasedonthegeneralizedexplicitmethodsforquasinonexpansivemappingsinbanachspaces AT thiernommsow modifiedmanniterativeschemebasedonthegeneralizedexplicitmethodsforquasinonexpansivemappingsinbanachspaces |