Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
<p/> <p>In the class of quasi-contractive operators satisfying Zamfirescu's conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent to the unique fixed point. In this paper, the comparison of the fir...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2004-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2004/716359 |
| _version_ | 1819140826122420224 |
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| author | Berinde Vasile |
| author_facet | Berinde Vasile |
| author_sort | Berinde Vasile |
| collection | DOAJ |
| description | <p/> <p>In the class of quasi-contractive operators satisfying Zamfirescu's conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent to the unique fixed point. In this paper, the comparison of the first two methods with respect to their convergence rate is obtained.</p> |
| first_indexed | 2024-12-22T11:44:43Z |
| format | Article |
| id | doaj.art-87aa9103d9df456ca5589cbda1c15e3c |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-22T11:44:43Z |
| publishDate | 2004-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-87aa9103d9df456ca5589cbda1c15e3c2022-12-21T18:27:09ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122004-01-0120042716359Picard iteration converges faster than Mann iteration for a class of quasi-contractive operatorsBerinde Vasile<p/> <p>In the class of quasi-contractive operators satisfying Zamfirescu's conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent to the unique fixed point. In this paper, the comparison of the first two methods with respect to their convergence rate is obtained.</p>http://www.fixedpointtheoryandapplications.com/content/2004/716359 |
| spellingShingle | Berinde Vasile Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators Fixed Point Theory and Applications |
| title | Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators |
| title_full | Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators |
| title_fullStr | Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators |
| title_full_unstemmed | Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators |
| title_short | Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators |
| title_sort | picard iteration converges faster than mann iteration for a class of quasi contractive operators |
| url | http://www.fixedpointtheoryandapplications.com/content/2004/716359 |
| work_keys_str_mv | AT berindevasile picarditerationconvergesfasterthanmanniterationforaclassofquasicontractiveoperators |