The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings
The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper studies the convergence analysis of the class of asymptotic...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/6876385 |
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| _version_ | 1850176756413104128 |
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| author | M. O. Aibinu S. C. Thakur S. Moyo |
| author_facet | M. O. Aibinu S. C. Thakur S. Moyo |
| author_sort | M. O. Aibinu |
| collection | DOAJ |
| description | The concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper studies the convergence analysis of the class of asymptotically nonexpansive mappings by the implicit midpoint iterative procedures. The necessary conditions for the convergence of the class of asymptotically nonexpansive mappings are established, by using a well-known iterative algorithm which plays important roles in the computation of fixed points of nonlinear mappings. A numerical example is presented to illustrate the convergence result. Under relaxed conditions on the parameters, some algorithms and strong convergence results were derived to obtain some results in the literature as corollaries. |
| format | Article |
| id | doaj-art-b8a1af8357184e6fb2fb903166e6383a |
| institution | OA Journals |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b8a1af8357184e6fb2fb903166e6383a2025-08-20T02:19:11ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/68763856876385The Implicit Midpoint Procedures for Asymptotically Nonexpansive MappingsM. O. Aibinu0S. C. Thakur1S. Moyo2Institute for Systems Science, Durban University of Technology, Durban 4000, South AfricaKZN CoLab, Durban University of Technology, Durban 4000, South AfricaInstitute for Systems Science & Office of the DVC Research, Innovation & Engagement Milena Court, Durban University of Technology, Durban 4000, South AfricaThe concept of asymptotically nonexpansive mappings is an important generalization of the class of nonexpansive mappings. Implicit midpoint procedures are extremely fundamental for solving equations involving nonlinear operators. This paper studies the convergence analysis of the class of asymptotically nonexpansive mappings by the implicit midpoint iterative procedures. The necessary conditions for the convergence of the class of asymptotically nonexpansive mappings are established, by using a well-known iterative algorithm which plays important roles in the computation of fixed points of nonlinear mappings. A numerical example is presented to illustrate the convergence result. Under relaxed conditions on the parameters, some algorithms and strong convergence results were derived to obtain some results in the literature as corollaries.http://dx.doi.org/10.1155/2020/6876385 |
| spellingShingle | M. O. Aibinu S. C. Thakur S. Moyo The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings Journal of Mathematics |
| title | The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings |
| title_full | The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings |
| title_fullStr | The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings |
| title_full_unstemmed | The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings |
| title_short | The Implicit Midpoint Procedures for Asymptotically Nonexpansive Mappings |
| title_sort | implicit midpoint procedures for asymptotically nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2020/6876385 |
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