On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals

We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster...

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Main Authors: Jukkrit Daengsaen, Anchalee Khemphet
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2018/7345401
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author Jukkrit Daengsaen
Anchalee Khemphet
author_facet Jukkrit Daengsaen
Anchalee Khemphet
author_sort Jukkrit Daengsaen
collection DOAJ
description We introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.
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publisher Wiley
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spelling doaj-art-e2f0a239f0754ff2b8b5e1ec01e24f2d2025-08-20T03:21:06ZengWileyAbstract and Applied Analysis1085-33751687-04092018-01-01201810.1155/2018/73454017345401On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed IntervalsJukkrit Daengsaen0Anchalee Khemphet1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandCenter of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandWe introduce a new iterative method called D-iteration to approximate a fixed point of continuous nondecreasing functions on arbitrary closed intervals. The purpose is to improve the rate of convergence compared to previous work. Specifically, our main result shows that D-iteration converges faster than P-iteration and SP-iteration to the fixed point. Consequently, we have that D-iteration converges faster than the others under the same computational cost. Moreover, the analogue of their convergence theorem holds for D-iteration.http://dx.doi.org/10.1155/2018/7345401
spellingShingle Jukkrit Daengsaen
Anchalee Khemphet
On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
Abstract and Applied Analysis
title On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_full On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_fullStr On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_full_unstemmed On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_short On the Rate of Convergence of P-Iteration, SP-Iteration, and D-Iteration Methods for Continuous Nondecreasing Functions on Closed Intervals
title_sort on the rate of convergence of p iteration sp iteration and d iteration methods for continuous nondecreasing functions on closed intervals
url http://dx.doi.org/10.1155/2018/7345401
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AT anchaleekhemphet ontherateofconvergenceofpiterationspiterationandditerationmethodsforcontinuousnondecreasingfunctionsonclosedintervals