Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method
The main intent of this article is to innovate a new iterative method to approximate fixed points of contraction and nonexpansive mappings. We prove that the new iterative method is stable for contraction and has a better rate of convergence than some distinctive iterative methods. Furthermore, some...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/6962430 |
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| _version_ | 1832552852861485056 |
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| author | Faizan Ahmad Khan |
| author_facet | Faizan Ahmad Khan |
| author_sort | Faizan Ahmad Khan |
| collection | DOAJ |
| description | The main intent of this article is to innovate a new iterative method to approximate fixed points of contraction and nonexpansive mappings. We prove that the new iterative method is stable for contraction and has a better rate of convergence than some distinctive iterative methods. Furthermore, some convergence results are proved for nonexpansive mappings. Finally, the solution of a nonlinear fractional difference equation is approximated via the proposed iterative method. Some numerical examples are constructed to support the analytical results and to illustrate the efficiency of the proposed iterative method. |
| format | Article |
| id | doaj-art-5ddb2f40fc0c438db5624e73a2edbd04 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-5ddb2f40fc0c438db5624e73a2edbd042025-02-03T05:57:38ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/6962430Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative MethodFaizan Ahmad Khan0Department of MathematicsThe main intent of this article is to innovate a new iterative method to approximate fixed points of contraction and nonexpansive mappings. We prove that the new iterative method is stable for contraction and has a better rate of convergence than some distinctive iterative methods. Furthermore, some convergence results are proved for nonexpansive mappings. Finally, the solution of a nonlinear fractional difference equation is approximated via the proposed iterative method. Some numerical examples are constructed to support the analytical results and to illustrate the efficiency of the proposed iterative method.http://dx.doi.org/10.1155/2022/6962430 |
| spellingShingle | Faizan Ahmad Khan Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method Journal of Mathematics |
| title | Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method |
| title_full | Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method |
| title_fullStr | Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method |
| title_full_unstemmed | Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method |
| title_short | Approximating Fixed Points and the Solution of a Nonlinear Fractional Difference Equation via an Iterative Method |
| title_sort | approximating fixed points and the solution of a nonlinear fractional difference equation via an iterative method |
| url | http://dx.doi.org/10.1155/2022/6962430 |
| work_keys_str_mv | AT faizanahmadkhan approximatingfixedpointsandthesolutionofanonlinearfractionaldifferenceequationviaaniterativemethod |