Recurrent Inequalities and Some of their Applications to Picard and Mann Iterations

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...

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Bibliographic Details
Main Authors: Berinde Vasile, Măruşter Ştefan
Format: Article
Language:English
Published: Sciendo 2014-06-01
Series:Annals of the West University of Timisoara: Mathematics and Computer Science
Subjects:
recurrent inequalities
fixed points
iterative procedures
Online Access:https://doi.org/10.2478/awutm-2014-0001
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spelling doaj-d64d0a8ecbee4e01bcf8193d15a36e122021-09-06T19:41:29ZengSciendoAnnals 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
collection DOAJ
language English
format Article
sources DOAJ
author Berinde Vasile
Măruşter Ştefan
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
author_facet Berinde Vasile
Măruşter Ştefan
author_sort Berinde Vasile
title 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_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_sort recurrent inequalities and some of their applications to picard and mann iterations
publisher Sciendo
series Annals of the West University of Timisoara: Mathematics and Computer Science
issn 1841-3307
publishDate 2014-06-01
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.
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
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