Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations
Two lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations are obtained for the Picard and Mann iterations in the case of demicontractive mappings. Additional conditions that ensure the strong convergen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2014-06-01
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| Series: | Annals of the West University of Timisoara: Mathematics and Computer Science |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/awutm-2014-0001 |
| _version_ | 1818477127975043072 |
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| author | Berinde Vasile Măruşter Ştefan |
| author_facet | Berinde Vasile Măruşter Ştefan |
| author_sort | Berinde Vasile |
| collection | DOAJ |
| description | Two lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations are obtained for the Picard and Mann iterations in the case of demicontractive mappings. Additional conditions that ensure the strong convergence in the same cases can be obtained on the basis of these lemmas. |
| first_indexed | 2024-12-10T09:34:12Z |
| format | Article |
| id | doaj.art-d64d0a8ecbee4e01bcf8193d15a36e12 |
| institution | Directory Open Access Journal |
| issn | 1841-3307 |
| language | English |
| last_indexed | 2024-12-10T09:34:12Z |
| publishDate | 2014-06-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Annals of the West University of Timisoara: Mathematics and Computer Science |
| spelling | doaj.art-d64d0a8ecbee4e01bcf8193d15a36e122022-12-22T01:54:14ZengSciendoAnnals of the West University of Timisoara: Mathematics and Computer Science1841-33072014-06-0152131610.2478/awutm-2014-0001awutm-2014-0001Recurrent Inequalities and Some of their Applications to Picard and Mann IterationsBerinde Vasile0Măruşter Ştefan1North University of Baia Mare, RomaniaWest University of Timişoara, RomaniaTwo lemmas concerning the superior bound of a numerical sequence satisfying a common recurrence inequality are given. As applications, the error estimations are obtained for the Picard and Mann iterations in the case of demicontractive mappings. Additional conditions that ensure the strong convergence in the same cases can be obtained on the basis of these lemmas.https://doi.org/10.2478/awutm-2014-0001recurrent inequalitiesfixed pointsiterative procedures |
| spellingShingle | Berinde Vasile Măruşter Ştefan Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations Annals of the West University of Timisoara: Mathematics and Computer Science recurrent inequalities fixed points iterative procedures |
| title | Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations |
| title_full | Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations |
| title_fullStr | Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations |
| title_full_unstemmed | Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations |
| title_short | Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations |
| title_sort | recurrent inequalities and some of their applications to picard and mann iterations |
| topic | recurrent inequalities fixed points iterative procedures |
| url | https://doi.org/10.2478/awutm-2014-0001 |
| work_keys_str_mv | AT berindevasile recurrentinequalitiesandsomeoftheirapplicationstopicardandmanniterations AT marusterstefan recurrentinequalitiesandsomeoftheirapplicationstopicardandmanniterations |