On analytical and numerical study of implicit fixed point iterations

On analytical and numerical study of implicit fixed point iterations

In this article, we define a new three-step implicit iteration and study its strong convergence, stability and data dependence. It is shown that the new three-step iteration has better rate of convergence than implicit and explicit Mann iterations as well as implicit Ishikawa-type iteration. Numeric...

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Bibliographic Details
Main Authors: Renu Chugh, Preety Malik, Vivek Kumar
Format: Article
Language:English
Published: Taylor & Francis Group 2015-12-01
Series:Cogent Mathematics
Subjects:
implicit iterations
strong convergence
convergence rate
stability
data dependence
Online Access:http://dx.doi.org/10.1080/23311835.2015.1021623
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spelling doaj-f875acb7f75343a0b55fc1ee2b88cda02020-11-25T02:01:16ZengTaylor & Francis GroupCogent Mathematics2331-18352015-12-012110.1080/23311835.2015.10216231021623On analytical and numerical study of implicit fixed point iterationsRenu Chugh0Preety Malik1Vivek Kumar2Maharshi Dayanand UniversityMaharshi Dayanand UniversityKLP CollegeIn this article, we define a new three-step implicit iteration and study its strong convergence, stability and data dependence. It is shown that the new three-step iteration has better rate of convergence than implicit and explicit Mann iterations as well as implicit Ishikawa-type iteration. Numerical example in support of validity of our results is provided.http://dx.doi.org/10.1080/23311835.2015.1021623implicit iterationsstrong convergenceconvergence ratestabilitydata dependence
collection DOAJ
language English
format Article
sources DOAJ
author Renu Chugh
Preety Malik
Vivek Kumar
spellingShingle Renu Chugh
Preety Malik
Vivek Kumar
On analytical and numerical study of implicit fixed point iterations
Cogent Mathematics
implicit iterations
strong convergence
convergence rate
stability
data dependence
author_facet Renu Chugh
Preety Malik
Vivek Kumar
author_sort Renu Chugh
title On analytical and numerical study of implicit fixed point iterations
title_short On analytical and numerical study of implicit fixed point iterations
title_full On analytical and numerical study of implicit fixed point iterations
title_fullStr On analytical and numerical study of implicit fixed point iterations
title_full_unstemmed On analytical and numerical study of implicit fixed point iterations
title_sort on analytical and numerical study of implicit fixed point iterations
publisher Taylor & Francis Group
series Cogent Mathematics
issn 2331-1835
publishDate 2015-12-01
description In this article, we define a new three-step implicit iteration and study its strong convergence, stability and data dependence. It is shown that the new three-step iteration has better rate of convergence than implicit and explicit Mann iterations as well as implicit Ishikawa-type iteration. Numerical example in support of validity of our results is provided.
topic implicit iterations
strong convergence
convergence rate
stability
data dependence
url http://dx.doi.org/10.1080/23311835.2015.1021623
work_keys_str_mv AT renuchugh onanalyticalandnumericalstudyofimplicitfixedpointiterations
AT preetymalik onanalyticalandnumericalstudyofimplicitfixedpointiterations
AT vivekkumar onanalyticalandnumericalstudyofimplicitfixedpointiterations
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