Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations
We consider the class of generalized α-nonexpansive mappings in a setting of Banach spaces. We prove existence of fixed point and convergence results for these mappings under the K∗-iterative process. The weak convergence is obtained with the help of Opial’s property while strong convergence results...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2023/8432560 |
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| author | Kifayat Ullah Sabri T. M. Thabet Anwar Kamal Junaid Ahmad Fayyaz Ahmad |
| author_facet | Kifayat Ullah Sabri T. M. Thabet Anwar Kamal Junaid Ahmad Fayyaz Ahmad |
| author_sort | Kifayat Ullah |
| collection | DOAJ |
| description | We consider the class of generalized α-nonexpansive mappings in a setting of Banach spaces. We prove existence of fixed point and convergence results for these mappings under the K∗-iterative process. The weak convergence is obtained with the help of Opial’s property while strong convergence results are obtained under various assumptions. Finally, we construct two numerical examples and connect our K∗-iterative process with them. An application to solve a fractional differential equation (FDE) is also provided. It has been eventually shown that the K∗- iterative process of this example gives more accurate numerical results corresponding to some other iterative processes of the literature. The main outcome is new and improves some known results of the literature. |
| format | Article |
| id | doaj-art-b67a281a8315410aa5417c1a03d2f0d3 |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-b67a281a8315410aa5417c1a03d2f0d32025-02-03T06:42:41ZengWileyDiscrete Dynamics in Nature and Society1607-887X2023-01-01202310.1155/2023/8432560Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential EquationsKifayat Ullah0Sabri T. M. Thabet1Anwar Kamal2Junaid Ahmad3Fayyaz Ahmad4Department of Mathematical SciencesDepartment of MathematicsDepartment of Mathematical SciencesDepartment of Mathematics and StatisticsDepartment of Mathematical SciencesWe consider the class of generalized α-nonexpansive mappings in a setting of Banach spaces. We prove existence of fixed point and convergence results for these mappings under the K∗-iterative process. The weak convergence is obtained with the help of Opial’s property while strong convergence results are obtained under various assumptions. Finally, we construct two numerical examples and connect our K∗-iterative process with them. An application to solve a fractional differential equation (FDE) is also provided. It has been eventually shown that the K∗- iterative process of this example gives more accurate numerical results corresponding to some other iterative processes of the literature. The main outcome is new and improves some known results of the literature.http://dx.doi.org/10.1155/2023/8432560 |
| spellingShingle | Kifayat Ullah Sabri T. M. Thabet Anwar Kamal Junaid Ahmad Fayyaz Ahmad Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations Discrete Dynamics in Nature and Society |
| title | Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations |
| title_full | Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations |
| title_fullStr | Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations |
| title_full_unstemmed | Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations |
| title_short | Convergence Analysis of an Iteration Process for a Class of Generalized Nonexpansive Mappings with Application to Fractional Differential Equations |
| title_sort | convergence analysis of an iteration process for a class of generalized nonexpansive mappings with application to fractional differential equations |
| url | http://dx.doi.org/10.1155/2023/8432560 |
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