New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities
In this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/5/1025 |
| _version_ | 1797495083681972224 |
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| author | Samet Maldar |
| author_facet | Samet Maldar |
| author_sort | Samet Maldar |
| collection | DOAJ |
| description | In this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that their convergence behavior is better than existing algorithms with non-simple samples. In addition, the concept of data dependency for these algorithms has been examined for the first time in this study. Finally, it has been proven that the solution of a variational inequality system can be obtained using newly defined parallel algorithms under suitable conditions. |
| first_indexed | 2024-03-10T01:43:22Z |
| format | Article |
| id | doaj.art-7dcf4da9dc414938a567dd53ae1694ae |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T01:43:22Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7dcf4da9dc414938a567dd53ae1694ae2023-11-23T13:20:11ZengMDPI AGSymmetry2073-89942022-05-01145102510.3390/sym14051025New Parallel Fixed Point Algorithms and Their Application to a System of Variational InequalitiesSamet Maldar0Department of Mathematics, Aksaray University, 68100 Aksaray, TurkeyIn this study, considering the advantages of parallel fixed point algorithms arising from their symmetrical behavior, new types of parallel algorithms have been defined. Strong convergence of these algorithms for certain mappings with altering points has been analyzed, and it has been observed that their convergence behavior is better than existing algorithms with non-simple samples. In addition, the concept of data dependency for these algorithms has been examined for the first time in this study. Finally, it has been proven that the solution of a variational inequality system can be obtained using newly defined parallel algorithms under suitable conditions.https://www.mdpi.com/2073-8994/14/5/1025iterative algorithmvariational inequalitiesrelaxed (<i>κ</i>, <i>ω</i>)-cocoercive mappingsnonexpansive mappings |
| spellingShingle | Samet Maldar New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities Symmetry iterative algorithm variational inequalities relaxed (<i>κ</i>, <i>ω</i>)-cocoercive mappings nonexpansive mappings |
| title | New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities |
| title_full | New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities |
| title_fullStr | New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities |
| title_full_unstemmed | New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities |
| title_short | New Parallel Fixed Point Algorithms and Their Application to a System of Variational Inequalities |
| title_sort | new parallel fixed point algorithms and their application to a system of variational inequalities |
| topic | iterative algorithm variational inequalities relaxed (<i>κ</i>, <i>ω</i>)-cocoercive mappings nonexpansive mappings |
| url | https://www.mdpi.com/2073-8994/14/5/1025 |
| work_keys_str_mv | AT sametmaldar newparallelfixedpointalgorithmsandtheirapplicationtoasystemofvariationalinequalities |