A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach Spaces
In this paper, we proposed a new iterative process to approximate fixed point of generalized $\alpha$-nonexpansivemappings and show that the coefficient used in the proposed iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new iterative pro...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2022-06-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_253544_425d0661899a3e86795c69cdcfeab4b3.pdf |
| _version_ | 1818018682891141120 |
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| author | Asghar Rahimi Ali Rezaei Bayaz Daraby Mostafa Ghasemi |
| author_facet | Asghar Rahimi Ali Rezaei Bayaz Daraby Mostafa Ghasemi |
| author_sort | Asghar Rahimi |
| collection | DOAJ |
| description | In this paper, we proposed a new iterative process to approximate fixed point of generalized $\alpha$-nonexpansivemappings and show that the coefficient used in the proposed iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new iterative process with other well-known iterative process by using numerical examples. Finally, by using new iterative process, we obtained some weak and strong convergence theorems for generalized $\alpha$-nonexpansive mappings in a Banach space. |
| first_indexed | 2024-04-14T07:43:20Z |
| format | Article |
| id | doaj.art-5c81de25c49d4c169a4465d9e1a2636e |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-04-14T07:43:20Z |
| publishDate | 2022-06-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-5c81de25c49d4c169a4465d9e1a2636e2022-12-22T02:05:26ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002022-06-011929111110.22130/scma.2022.548031.1057253544A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach SpacesAsghar Rahimi0Ali Rezaei1Bayaz Daraby2Mostafa Ghasemi3Department of Mathematics, University of Maragheh, Maragheh, Iran.Department of Mathematics, University of Maragheh, Maragheh, IranDepartment of Mathematics, University of Maragheh, Maragheh, Iran.Department of Mathematics, University of Maragheh, Maragheh, Iran.In this paper, we proposed a new iterative process to approximate fixed point of generalized $\alpha$-nonexpansivemappings and show that the coefficient used in the proposed iterative process play a fundamental role in the rate of convergence. We compare the speed of convergence of new iterative process with other well-known iterative process by using numerical examples. Finally, by using new iterative process, we obtained some weak and strong convergence theorems for generalized $\alpha$-nonexpansive mappings in a Banach space.https://scma.maragheh.ac.ir/article_253544_425d0661899a3e86795c69cdcfeab4b3.pdfuniformly convex banach spaceweak convergencestrong convergencegeneralized $alpha$-nonexpansive mappingiterative processquasi-nonexpansive mapping |
| spellingShingle | Asghar Rahimi Ali Rezaei Bayaz Daraby Mostafa Ghasemi A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach Spaces Sahand Communications in Mathematical Analysis uniformly convex banach space weak convergence strong convergence generalized $alpha$-nonexpansive mapping iterative process quasi-nonexpansive mapping |
| title | A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach Spaces |
| title_full | A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach Spaces |
| title_fullStr | A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach Spaces |
| title_short | A New and Faster Iterative Scheme Including Generalized $\alpha$-nonexpansive Mappings in Banach Spaces |
| title_sort | new and faster iterative scheme including generalized alpha nonexpansive mappings in banach spaces |
| topic | uniformly convex banach space weak convergence strong convergence generalized $alpha$-nonexpansive mapping iterative process quasi-nonexpansive mapping |
| url | https://scma.maragheh.ac.ir/article_253544_425d0661899a3e86795c69cdcfeab4b3.pdf |
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