Approximating Fixed Points of Generalized $\alpha-$Nonexpansive Mappings by the New Iteration Process
In this paper we introduce a new iteration process for approximation of fixed points. We numerically compare convergence behavior of our iteration process with other iteration process like M-iteration process. We also prove weak and strong convergence theorems for generalized $\alpha-$nonexpansive...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Mahmut Akyigit
2022-04-01
|
| Series: | Journal of Mathematical Sciences and Modelling |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1968138 |
| _version_ | 1797352505273745408 |
|---|---|
| author | Öznur Korkut Seyit Temir |
| author_facet | Öznur Korkut Seyit Temir |
| author_sort | Öznur Korkut |
| collection | DOAJ |
| description | In this paper we introduce a new iteration process for approximation of fixed points. We numerically compare convergence behavior of our iteration process with other iteration process like M-iteration process. We also prove weak and strong convergence theorems for generalized $\alpha-$nonexpansive mappings by using new iteration process. Furthermore we give an example for generalized $\alpha-$nonexpansive mapping but does not satisfy $(C)$ condition. |
| first_indexed | 2024-03-08T13:16:30Z |
| format | Article |
| id | doaj.art-97bdfa102f9e41f181fca1da2198b73c |
| institution | Directory Open Access Journal |
| issn | 2636-8692 |
| language | English |
| last_indexed | 2024-03-08T13:16:30Z |
| publishDate | 2022-04-01 |
| publisher | Mahmut Akyigit |
| record_format | Article |
| series | Journal of Mathematical Sciences and Modelling |
| spelling | doaj.art-97bdfa102f9e41f181fca1da2198b73c2024-01-18T06:28:18ZengMahmut AkyigitJournal of Mathematical Sciences and Modelling2636-86922022-04-015135391408Approximating Fixed Points of Generalized $\alpha-$Nonexpansive Mappings by the New Iteration ProcessÖznur KorkutSeyit Temir0ADIYAMAN UNIVERSITYIn this paper we introduce a new iteration process for approximation of fixed points. We numerically compare convergence behavior of our iteration process with other iteration process like M-iteration process. We also prove weak and strong convergence theorems for generalized $\alpha-$nonexpansive mappings by using new iteration process. Furthermore we give an example for generalized $\alpha-$nonexpansive mapping but does not satisfy $(C)$ condition.https://dergipark.org.tr/tr/download/article-file/1968138uniformly convex banach spacesiteration processesgeneralized $\alpha-$nonexpansive mappingsfixed pointconvergence |
| spellingShingle | Öznur Korkut Seyit Temir Approximating Fixed Points of Generalized $\alpha-$Nonexpansive Mappings by the New Iteration Process Journal of Mathematical Sciences and Modelling uniformly convex banach spaces iteration processes generalized $\alpha-$nonexpansive mappings fixed point convergence |
| title | Approximating Fixed Points of Generalized $\alpha-$Nonexpansive Mappings by the New Iteration Process |
| title_full | Approximating Fixed Points of Generalized $\alpha-$Nonexpansive Mappings by the New Iteration Process |
| title_fullStr | Approximating Fixed Points of Generalized $\alpha-$Nonexpansive Mappings by the New Iteration Process |
| title_full_unstemmed | Approximating Fixed Points of Generalized $\alpha-$Nonexpansive Mappings by the New Iteration Process |
| title_short | Approximating Fixed Points of Generalized $\alpha-$Nonexpansive Mappings by the New Iteration Process |
| title_sort | approximating fixed points of generalized alpha nonexpansive mappings by the new iteration process |
| topic | uniformly convex banach spaces iteration processes generalized $\alpha-$nonexpansive mappings fixed point convergence |
| url | https://dergipark.org.tr/tr/download/article-file/1968138 |
| work_keys_str_mv | AT oznurkorkut approximatingfixedpointsofgeneralizedalphanonexpansivemappingsbythenewiterationprocess AT seyittemir approximatingfixedpointsofgeneralizedalphanonexpansivemappingsbythenewiterationprocess |