On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application
In this article, we considered the class of generalized α,β-nonexpansive (GABN) mappings that properly includes all nonexpansive, Suzuki nonexpansive (SN), generalized α-nonexpansive (GAN), and Reich–Suzuki nonexpansive (RSN) mappings. We used the iterative scheme JA for finding fixed points of thes...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/5459916 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850177869344407552 |
|---|---|
| author | Fayyaz Ahmad Kifayat Ullah Junaid Ahmad Om Kalthum S. K. Mohamed Awad A. Bakery |
| author_facet | Fayyaz Ahmad Kifayat Ullah Junaid Ahmad Om Kalthum S. K. Mohamed Awad A. Bakery |
| author_sort | Fayyaz Ahmad |
| collection | DOAJ |
| description | In this article, we considered the class of generalized α,β-nonexpansive (GABN) mappings that properly includes all nonexpansive, Suzuki nonexpansive (SN), generalized α-nonexpansive (GAN), and Reich–Suzuki nonexpansive (RSN) mappings. We used the iterative scheme JA for finding fixed points of these mappings in a Banach space setting. We provided both weak and strong convergence results under some mild conditions on the mapping, domain, and on the parameters involved in our iterative scheme. To support these results numerically, we constructed a new example of GABN mappings and proved that the JA iterative scheme converges to its fixed point. Moreover, we proved that JA iterative scheme converges faster to the fixed point corresponding to the some other iterative schemes of the literature. Eventually, we carried out an application of our main outcome to solve a split feasibility of problems (SFPs) in the setting of GABN mappings. Thus, our results were new in the literature and improved well-known results of the literature. |
| format | Article |
| id | doaj-art-c3298596aac04fafbf497f9e293c1c83 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-c3298596aac04fafbf497f9e293c1c832025-08-20T02:18:54ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/5459916On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive ApplicationFayyaz Ahmad0Kifayat Ullah1Junaid Ahmad2Om Kalthum S. K. Mohamed3Awad A. Bakery4Department of Mathematical SciencesDepartment of Mathematical SciencesDepartment of MathematicsUniversity of JeddahUniversity of JeddahIn this article, we considered the class of generalized α,β-nonexpansive (GABN) mappings that properly includes all nonexpansive, Suzuki nonexpansive (SN), generalized α-nonexpansive (GAN), and Reich–Suzuki nonexpansive (RSN) mappings. We used the iterative scheme JA for finding fixed points of these mappings in a Banach space setting. We provided both weak and strong convergence results under some mild conditions on the mapping, domain, and on the parameters involved in our iterative scheme. To support these results numerically, we constructed a new example of GABN mappings and proved that the JA iterative scheme converges to its fixed point. Moreover, we proved that JA iterative scheme converges faster to the fixed point corresponding to the some other iterative schemes of the literature. Eventually, we carried out an application of our main outcome to solve a split feasibility of problems (SFPs) in the setting of GABN mappings. Thus, our results were new in the literature and improved well-known results of the literature.http://dx.doi.org/10.1155/2023/5459916 |
| spellingShingle | Fayyaz Ahmad Kifayat Ullah Junaid Ahmad Om Kalthum S. K. Mohamed Awad A. Bakery On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application Journal of Mathematics |
| title | On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application |
| title_full | On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application |
| title_fullStr | On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application |
| title_full_unstemmed | On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application |
| title_short | On Fixed Point Convergence Results for a General Class of Nonlinear Mappings with a Supportive Application |
| title_sort | on fixed point convergence results for a general class of nonlinear mappings with a supportive application |
| url | http://dx.doi.org/10.1155/2023/5459916 |
| work_keys_str_mv | AT fayyazahmad onfixedpointconvergenceresultsforageneralclassofnonlinearmappingswithasupportiveapplication AT kifayatullah onfixedpointconvergenceresultsforageneralclassofnonlinearmappingswithasupportiveapplication AT junaidahmad onfixedpointconvergenceresultsforageneralclassofnonlinearmappingswithasupportiveapplication AT omkalthumskmohamed onfixedpointconvergenceresultsforageneralclassofnonlinearmappingswithasupportiveapplication AT awadabakery onfixedpointconvergenceresultsforageneralclassofnonlinearmappingswithasupportiveapplication |