On the Rate of Convergence of Kirk-Type Iterative Schemes

On the Rate of Convergence of Kirk-Type Iterative Schemes

The purpose of this paper is to introduce Kirk-type new iterative schemes called Kirk-SP and Kirk-CR schemes and to study the convergence of these iterative schemes by employing certain quasi-contractive operators. By taking an example, we will compare Kirk-SP, Kirk-CR, Kirk-Mann, Kirk-Ishikawa, a...

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Main Authors: Nawab Hussain, Renu Chugh, Vivek Kumar, Arif Rafiq
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/526503
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spelling doaj-cf4e4b2f14c348439e8159a177813d562020-11-24T20:40:22ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/526503526503On the Rate of Convergence of Kirk-Type Iterative SchemesNawab Hussain0Renu Chugh1Vivek Kumar2Arif Rafiq3Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, M. D. University, Rohtak 124001, IndiaDepartment of Mathematics, M. D. University, Rohtak 124001, IndiaHajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, PakistanThe purpose of this paper is to introduce Kirk-type new iterative schemes called Kirk-SP and Kirk-CR schemes and to study the convergence of these iterative schemes by employing certain quasi-contractive operators. By taking an example, we will compare Kirk-SP, Kirk-CR, Kirk-Mann, Kirk-Ishikawa, and Kirk-Noor iterative schemes for aforementioned class of operators. Also, using computer programs in C++, we compare the above-mentioned iterative schemes through examples of increasing, decreasing, sublinear, superlinear, and oscillatory functions.http://dx.doi.org/10.1155/2012/526503
collection DOAJ
language English
format Article
sources DOAJ
author Nawab Hussain
Renu Chugh
Vivek Kumar
Arif Rafiq
spellingShingle Nawab Hussain
Renu Chugh
Vivek Kumar
Arif Rafiq
On the Rate of Convergence of Kirk-Type Iterative Schemes
Journal of Applied Mathematics
author_facet Nawab Hussain
Renu Chugh
Vivek Kumar
Arif Rafiq
author_sort Nawab Hussain
title On the Rate of Convergence of Kirk-Type Iterative Schemes
title_short On the Rate of Convergence of Kirk-Type Iterative Schemes
title_full On the Rate of Convergence of Kirk-Type Iterative Schemes
title_fullStr On the Rate of Convergence of Kirk-Type Iterative Schemes
title_full_unstemmed On the Rate of Convergence of Kirk-Type Iterative Schemes
title_sort on the rate of convergence of kirk-type iterative schemes
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description The purpose of this paper is to introduce Kirk-type new iterative schemes called Kirk-SP and Kirk-CR schemes and to study the convergence of these iterative schemes by employing certain quasi-contractive operators. By taking an example, we will compare Kirk-SP, Kirk-CR, Kirk-Mann, Kirk-Ishikawa, and Kirk-Noor iterative schemes for aforementioned class of operators. Also, using computer programs in C++, we compare the above-mentioned iterative schemes through examples of increasing, decreasing, sublinear, superlinear, and oscillatory functions.
url http://dx.doi.org/10.1155/2012/526503
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AT renuchugh ontherateofconvergenceofkirktypeiterativeschemes
AT vivekkumar ontherateofconvergenceofkirktypeiterativeschemes
AT arifrafiq ontherateofconvergenceofkirktypeiterativeschemes
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