On the JK Iterative Process in Banach Spaces
In the recent progress, different iterative procedures have been constructed in order to find the fixed point for a given self-map in an effective way. Among the other things, an effective iterative procedure called the JK iterative scheme was recently constructed and its strong and weak convergence...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/2500421 |
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| author | Junaid Ahmad Hüseyin Işık Faeem Ali Kifayat Ullah Eskandar Ameer Muhammad Arshad |
| author_facet | Junaid Ahmad Hüseyin Işık Faeem Ali Kifayat Ullah Eskandar Ameer Muhammad Arshad |
| author_sort | Junaid Ahmad |
| collection | DOAJ |
| description | In the recent progress, different iterative procedures have been constructed in order to find the fixed point for a given self-map in an effective way. Among the other things, an effective iterative procedure called the JK iterative scheme was recently constructed and its strong and weak convergence was established for the class of Suzuki mappings in the setting of Banach spaces. The first purpose of this research is to obtain the strong and weak convergence of this scheme in the wider setting of generalized α-nonexpansive mappings. Secondly, by constructing an example of generalized α-nonexpansive maps which is not a Suzuki map, we show that the JK iterative scheme converges faster as compared the other iterative schemes. The presented results of this paper properly extend and improve the corresponding results of the literature. |
| format | Article |
| id | doaj-art-4f6770f3ce764045ad4fa0668d340fd0 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-4f6770f3ce764045ad4fa0668d340fd02025-02-03T01:25:09ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/25004212500421On the JK Iterative Process in Banach SpacesJunaid Ahmad0Hüseyin Işık1Faeem Ali2Kifayat Ullah3Eskandar Ameer4Muhammad Arshad5Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, PakistanDepartment of Engineering Science, Bandırma Onyedi Eylül University, Bandırma 10200, Balıkesir, TurkeyDepartment of Mathematics, Central University of Karnataka, Kalaburagi 585367, IndiaDepartment of Mathematics, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, Taiz University, Taiz, YemenDepartment of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, PakistanIn the recent progress, different iterative procedures have been constructed in order to find the fixed point for a given self-map in an effective way. Among the other things, an effective iterative procedure called the JK iterative scheme was recently constructed and its strong and weak convergence was established for the class of Suzuki mappings in the setting of Banach spaces. The first purpose of this research is to obtain the strong and weak convergence of this scheme in the wider setting of generalized α-nonexpansive mappings. Secondly, by constructing an example of generalized α-nonexpansive maps which is not a Suzuki map, we show that the JK iterative scheme converges faster as compared the other iterative schemes. The presented results of this paper properly extend and improve the corresponding results of the literature.http://dx.doi.org/10.1155/2021/2500421 |
| spellingShingle | Junaid Ahmad Hüseyin Işık Faeem Ali Kifayat Ullah Eskandar Ameer Muhammad Arshad On the JK Iterative Process in Banach Spaces Journal of Function Spaces |
| title | On the JK Iterative Process in Banach Spaces |
| title_full | On the JK Iterative Process in Banach Spaces |
| title_fullStr | On the JK Iterative Process in Banach Spaces |
| title_full_unstemmed | On the JK Iterative Process in Banach Spaces |
| title_short | On the JK Iterative Process in Banach Spaces |
| title_sort | on the jk iterative process in banach spaces |
| url | http://dx.doi.org/10.1155/2021/2500421 |
| work_keys_str_mv | AT junaidahmad onthejkiterativeprocessinbanachspaces AT huseyinisık onthejkiterativeprocessinbanachspaces AT faeemali onthejkiterativeprocessinbanachspaces AT kifayatullah onthejkiterativeprocessinbanachspaces AT eskandarameer onthejkiterativeprocessinbanachspaces AT muhammadarshad onthejkiterativeprocessinbanachspaces |