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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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2018/7345401 |
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| _version_ | 1849691224875728896 |
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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. |
| format | Article |
| id | doaj-art-e2f0a239f0754ff2b8b5e1ec01e24f2d |
| institution | DOAJ |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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 |
| work_keys_str_mv | AT jukkritdaengsaen ontherateofconvergenceofpiterationspiterationandditerationmethodsforcontinuousnondecreasingfunctionsonclosedintervals AT anchaleekhemphet ontherateofconvergenceofpiterationspiterationandditerationmethodsforcontinuousnondecreasingfunctionsonclosedintervals |