Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach space
In this paper, we establish strong and weak convergence theorems for Suzuki's generalized nonexpansive mapping in uniformly convex Banach spaces using the iterative scheme introduced by Panigrahy et al [9]. Next, we see an example of Suzuki's generalized nonexpansive mapping, which is not...
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University of Mohaghegh Ardabili
2024-06-01
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| Series: | Journal of Hyperstructures |
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| Online Access: | https://jhs.uma.ac.ir/article_3046_ce811fa337657db861dd22b49835ea04.pdf |
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| author | Omprash Sahu Amitabh Banerjee |
| author_facet | Omprash Sahu Amitabh Banerjee |
| author_sort | Omprash Sahu |
| collection | DOAJ |
| description | In this paper, we establish strong and weak convergence theorems for Suzuki's generalized nonexpansive mapping in uniformly convex Banach spaces using the iterative scheme introduced by Panigrahy et al [9]. Next, we see an example of Suzuki's generalized nonexpansive mapping, which is not a nonexpansive mapping. Using this example and some numerical tests, we infer empirically that the Panigrahy iteration process converges faster than the Krasnoselskij, Thakur, and M-iteration processes. |
| format | Article |
| id | doaj-art-46c71aa4649b43cabe3f2d36413d0328 |
| institution | DOAJ |
| issn | 2251-8436 2322-1666 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | University of Mohaghegh Ardabili |
| record_format | Article |
| series | Journal of Hyperstructures |
| spelling | doaj-art-46c71aa4649b43cabe3f2d36413d03282025-08-20T02:40:21ZengUniversity of Mohaghegh ArdabiliJournal of Hyperstructures2251-84362322-16662024-06-011319410810.22098/jhs.2024.14426.10053046Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach spaceOmprash Sahu0Amitabh Banerjee1Department of Mathematics, Babu Pandhri Rao Kridatt Govt.College Silouti, Dhamtari, Raipur(C.G.), IndiaPrincipal, Govt. J.Y. Chhattisgarh College, Raipur, IndiaIn this paper, we establish strong and weak convergence theorems for Suzuki's generalized nonexpansive mapping in uniformly convex Banach spaces using the iterative scheme introduced by Panigrahy et al [9]. Next, we see an example of Suzuki's generalized nonexpansive mapping, which is not a nonexpansive mapping. Using this example and some numerical tests, we infer empirically that the Panigrahy iteration process converges faster than the Krasnoselskij, Thakur, and M-iteration processes.https://jhs.uma.ac.ir/article_3046_ce811fa337657db861dd22b49835ea04.pdffixed pointuniformly convex banach spacesuzuki generalized nonexpansive mappingpanigrahy iterationconvergence theorem |
| spellingShingle | Omprash Sahu Amitabh Banerjee Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach space Journal of Hyperstructures fixed point uniformly convex banach space suzuki generalized nonexpansive mapping panigrahy iteration convergence theorem |
| title | Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach space |
| title_full | Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach space |
| title_fullStr | Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach space |
| title_full_unstemmed | Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach space |
| title_short | Convergence of Panigrahy iteration process for Suzuki generalized nonexpansive mapping in uniformly convex Banach space |
| title_sort | convergence of panigrahy iteration process for suzuki generalized nonexpansive mapping in uniformly convex banach space |
| topic | fixed point uniformly convex banach space suzuki generalized nonexpansive mapping panigrahy iteration convergence theorem |
| url | https://jhs.uma.ac.ir/article_3046_ce811fa337657db861dd22b49835ea04.pdf |
| work_keys_str_mv | AT omprashsahu convergenceofpanigrahyiterationprocessforsuzukigeneralizednonexpansivemappinginuniformlyconvexbanachspace AT amitabhbanerjee convergenceofpanigrahyiterationprocessforsuzukigeneralizednonexpansivemappinginuniformlyconvexbanachspace |