Thakur’s Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive Mappings
In this work, we propose the three-step Thakur iterative process associated with two mappings in the setting of Banach space. Using this Thakur iteration, we approximate a common fixed point for a pair of noncyclic, relatively nonexpansive mappings. And we support our main result with a numerical ex...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/5537768 |
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| author | R. Gopi V. Pragadeeswarar M. De La Sen |
| author_facet | R. Gopi V. Pragadeeswarar M. De La Sen |
| author_sort | R. Gopi |
| collection | DOAJ |
| description | In this work, we propose the three-step Thakur iterative process associated with two mappings in the setting of Banach space. Using this Thakur iteration, we approximate a common fixed point for a pair of noncyclic, relatively nonexpansive mappings. And we support our main result with a numerical example. Also, we give a stronger version of our main result by using von Neumann sequences. Finally, we provide some corollaries on the convergence of common best proximity points in uniformly convex Banach space. |
| format | Article |
| id | doaj-art-39b188709c0b4f1ea42e15df517ec0e7 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-39b188709c0b4f1ea42e15df517ec0e72025-08-20T03:55:11ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/5537768Thakur’s Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive MappingsR. Gopi0V. Pragadeeswarar1M. De La Sen2Department of MathematicsDepartment of MathematicsInstitute of Research and Development of Processes IIDPIn this work, we propose the three-step Thakur iterative process associated with two mappings in the setting of Banach space. Using this Thakur iteration, we approximate a common fixed point for a pair of noncyclic, relatively nonexpansive mappings. And we support our main result with a numerical example. Also, we give a stronger version of our main result by using von Neumann sequences. Finally, we provide some corollaries on the convergence of common best proximity points in uniformly convex Banach space.http://dx.doi.org/10.1155/2022/5537768 |
| spellingShingle | R. Gopi V. Pragadeeswarar M. De La Sen Thakur’s Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive Mappings Journal of Mathematics |
| title | Thakur’s Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive Mappings |
| title_full | Thakur’s Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive Mappings |
| title_fullStr | Thakur’s Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive Mappings |
| title_full_unstemmed | Thakur’s Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive Mappings |
| title_short | Thakur’s Iterative Scheme for Approximating Common Fixed Points to a Pair of Relatively Nonexpansive Mappings |
| title_sort | thakur s iterative scheme for approximating common fixed points to a pair of relatively nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2022/5537768 |
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