Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces
We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in 𝑞-uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/474031 |
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| _version_ | 1832552337218994176 |
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| author | Meng Wen Changsong Hu Zhiyu Wu |
| author_facet | Meng Wen Changsong Hu Zhiyu Wu |
| author_sort | Meng Wen |
| collection | DOAJ |
| description | We introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in 𝑞-uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others. |
| format | Article |
| id | doaj-art-053c70bee18f42bda0485909c5e02500 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-053c70bee18f42bda0485909c5e025002025-02-03T05:58:51ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/474031474031Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach SpacesMeng Wen0Changsong Hu1Zhiyu Wu2Department of Mathematics, Hubei Normal University, Hubei, Huangshi 435002, ChinaDepartment of Mathematics, Hubei Normal University, Hubei, Huangshi 435002, ChinaDepartment of Mathematics, Hubei Normal University, Hubei, Huangshi 435002, ChinaWe introduce a new iterative scheme with Meir-Keeler contractions for an asymptotically nonexpansive mapping in 𝑞-uniformly smooth and strictly convex Banach spaces. We also proved the strong convergence theorems of implicit and explicit schemes. The results obtained in this paper extend and improve many recent ones announced by many others.http://dx.doi.org/10.1155/2012/474031 |
| spellingShingle | Meng Wen Changsong Hu Zhiyu Wu Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces Journal of Applied Mathematics |
| title | Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces |
| title_full | Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces |
| title_fullStr | Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces |
| title_full_unstemmed | Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces |
| title_short | Convergence of Implicit and Explicit Schemes for an Asymptotically Nonexpansive Mapping in 𝑞-Uniformly Smooth and Strictly Convex Banach Spaces |
| title_sort | convergence of implicit and explicit schemes for an asymptotically nonexpansive mapping in 𝑞 uniformly smooth and strictly convex banach spaces |
| url | http://dx.doi.org/10.1155/2012/474031 |
| work_keys_str_mv | AT mengwen convergenceofimplicitandexplicitschemesforanasymptoticallynonexpansivemappinginquniformlysmoothandstrictlyconvexbanachspaces AT changsonghu convergenceofimplicitandexplicitschemesforanasymptoticallynonexpansivemappinginquniformlysmoothandstrictlyconvexbanachspaces AT zhiyuwu convergenceofimplicitandexplicitschemesforanasymptoticallynonexpansivemappinginquniformlysmoothandstrictlyconvexbanachspaces |