Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces
In this paper, we establish weak and strong convergence theorems for mean nonexpansive maps in Banach spaces under the Picard–Mann hybrid iteration process. We also construct an example of mean nonexpansive mappings and show that it exceeds the class of nonexpansive mappings. To show the numerical a...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/1934274 |
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| _version_ | 1832546044620046336 |
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| author | Junaid Ahmad Kifayat Ullah Muhammad Arshad Manuel de la Sen |
| author_facet | Junaid Ahmad Kifayat Ullah Muhammad Arshad Manuel de la Sen |
| author_sort | Junaid Ahmad |
| collection | DOAJ |
| description | In this paper, we establish weak and strong convergence theorems for mean nonexpansive maps in Banach spaces under the Picard–Mann hybrid iteration process. We also construct an example of mean nonexpansive mappings and show that it exceeds the class of nonexpansive mappings. To show the numerical accuracy of our main outcome, we show that Picard–Mann hybrid iteration process of this example is more effective than all of the Picard, Mann, and Ishikawa iterative processes. |
| format | Article |
| id | doaj-art-2658a43d23c34b05a7a2cbe3b34ba8de |
| 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-2658a43d23c34b05a7a2cbe3b34ba8de2025-02-03T07:23:54ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/19342741934274Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach SpacesJunaid Ahmad0Kifayat Ullah1Muhammad Arshad2Manuel de la Sen3Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, PakistanDepartment of Mathematics, University of Lakki Marwat, Lakki Marwat, 28420 Khyber Pakhtunkhwa, PakistanDepartment of Mathematics and Statistics, International Islamic University, H-10, Islamabad 44000, PakistanInstitute of Research and Development of Processes, University of the Basque Country, Campus of Leioa (Bizkaia), P.O. Box 644-Bilbao, Barrio Sarriena, 48940 Leioa, SpainIn this paper, we establish weak and strong convergence theorems for mean nonexpansive maps in Banach spaces under the Picard–Mann hybrid iteration process. We also construct an example of mean nonexpansive mappings and show that it exceeds the class of nonexpansive mappings. To show the numerical accuracy of our main outcome, we show that Picard–Mann hybrid iteration process of this example is more effective than all of the Picard, Mann, and Ishikawa iterative processes.http://dx.doi.org/10.1155/2021/1934274 |
| spellingShingle | Junaid Ahmad Kifayat Ullah Muhammad Arshad Manuel de la Sen Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces Journal of Function Spaces |
| title | Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces |
| title_full | Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces |
| title_fullStr | Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces |
| title_short | Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces |
| title_sort | approximation of fixed points for mean nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2021/1934274 |
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