On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces
In this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process. Using a numerical example, we prove that the Picard–Krasnoselskii hyb...
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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/10.1155/2020/2150748 |
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| _version_ | 1832568661052751872 |
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| author | Thabet Abdeljawad Kifayat Ullah Junaid Ahmad |
| author_facet | Thabet Abdeljawad Kifayat Ullah Junaid Ahmad |
| author_sort | Thabet Abdeljawad |
| collection | DOAJ |
| description | In this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process. Using a numerical example, we prove that the Picard–Krasnoselskii hybrid iteration process converges faster than both of the Picard and Krasnoselskii iteration processes. Our results are the extension and improvement of many well-known results of the literature. |
| format | Article |
| id | doaj-art-b2f211bd60e04044a13da91976725e36 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-b2f211bd60e04044a13da91976725e362025-02-03T00:58:41ZengWileyJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/21507482150748On Picard–Krasnoselskii Hybrid Iteration Process in Banach SpacesThabet Abdeljawad0Kifayat Ullah1Junaid Ahmad2Department of Mathematics and General Sciences, Prince Sultan University, P.O.Box. 66833, Riyadh 11586, Saudi ArabiaDepartment of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, PakistanDepartment of Mathematics, University of Science and Technology, Bannu 28100, Khyber Pakhtunkhwa, PakistanIn this research, we prove strong and weak convergence results for a class of mappings which is much more general than that of Suzuki nonexpansive mappings on Banach space through the Picard–Krasnoselskii hybrid iteration process. Using a numerical example, we prove that the Picard–Krasnoselskii hybrid iteration process converges faster than both of the Picard and Krasnoselskii iteration processes. Our results are the extension and improvement of many well-known results of the literature.http://dx.doi.org/10.1155/2020/2150748 |
| spellingShingle | Thabet Abdeljawad Kifayat Ullah Junaid Ahmad On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces Journal of Mathematics |
| title | On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces |
| title_full | On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces |
| title_fullStr | On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces |
| title_full_unstemmed | On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces |
| title_short | On Picard–Krasnoselskii Hybrid Iteration Process in Banach Spaces |
| title_sort | on picard krasnoselskii hybrid iteration process in banach spaces |
| url | http://dx.doi.org/10.1155/2020/2150748 |
| work_keys_str_mv | AT thabetabdeljawad onpicardkrasnoselskiihybriditerationprocessinbanachspaces AT kifayatullah onpicardkrasnoselskiihybriditerationprocessinbanachspaces AT junaidahmad onpicardkrasnoselskiihybriditerationprocessinbanachspaces |