A better iterative algorithm for fixed-point problem in Banach spaces with application
In this research article, we explore convergence results within the framework of Banach spaces by focusing on a specific iterative scheme, namely the T-iterative algorithm (TIA). Utilizing the Chatterjea–Suzuki-C (CSC) condition, we establish both strong and weak convergence. To validate the efficac...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001020 |
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| author | Wakeel Ahmed Shahid Zaman Tamseela Ashraf Asma Raza |
| author_facet | Wakeel Ahmed Shahid Zaman Tamseela Ashraf Asma Raza |
| author_sort | Wakeel Ahmed |
| collection | DOAJ |
| description | In this research article, we explore convergence results within the framework of Banach spaces by focusing on a specific iterative scheme, namely the T-iterative algorithm (TIA). Utilizing the Chatterjea–Suzuki-C (CSC) condition, we establish both strong and weak convergence. To validate the efficacy of our proposed iterative schemes, we conduct numerical experiments using MATLAB R2021a, demonstrating that our approach achieves a faster rate of convergence compared to existing methods. Furthermore, we give a clear example of complete mappings that satisfy the CSC condition whose fixed point is unique. As a practical application, we apply the main results to solve functional and fractional differential equations (FDEs), illustrating the broader applicability of our findings. |
| format | Article |
| id | doaj-art-af9e4f98a3434ed4ab699ffa588f34a0 |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-af9e4f98a3434ed4ab699ffa588f34a02025-08-20T02:31:09ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410117510.1016/j.padiff.2025.101175A better iterative algorithm for fixed-point problem in Banach spaces with applicationWakeel Ahmed0Shahid Zaman1Tamseela Ashraf2Asma Raza3Department of Mathematics, University of Sialkot, Sialkot 51310, Pakistan; Corresponding author.Department of Mathematical and Physical Sciences, University of Nizwa, Nizwa, OmanDepartment of Mathematics, University of Sialkot, Sialkot 51310, PakistanDepartment of Mathematics, University of Sialkot, Sialkot 51310, PakistanIn this research article, we explore convergence results within the framework of Banach spaces by focusing on a specific iterative scheme, namely the T-iterative algorithm (TIA). Utilizing the Chatterjea–Suzuki-C (CSC) condition, we establish both strong and weak convergence. To validate the efficacy of our proposed iterative schemes, we conduct numerical experiments using MATLAB R2021a, demonstrating that our approach achieves a faster rate of convergence compared to existing methods. Furthermore, we give a clear example of complete mappings that satisfy the CSC condition whose fixed point is unique. As a practical application, we apply the main results to solve functional and fractional differential equations (FDEs), illustrating the broader applicability of our findings.http://www.sciencedirect.com/science/article/pii/S2666818125001020Iterative algorithmCSC conditionConvergence theoremFixed pointBanach space |
| spellingShingle | Wakeel Ahmed Shahid Zaman Tamseela Ashraf Asma Raza A better iterative algorithm for fixed-point problem in Banach spaces with application Partial Differential Equations in Applied Mathematics Iterative algorithm CSC condition Convergence theorem Fixed point Banach space |
| title | A better iterative algorithm for fixed-point problem in Banach spaces with application |
| title_full | A better iterative algorithm for fixed-point problem in Banach spaces with application |
| title_fullStr | A better iterative algorithm for fixed-point problem in Banach spaces with application |
| title_full_unstemmed | A better iterative algorithm for fixed-point problem in Banach spaces with application |
| title_short | A better iterative algorithm for fixed-point problem in Banach spaces with application |
| title_sort | better iterative algorithm for fixed point problem in banach spaces with application |
| topic | Iterative algorithm CSC condition Convergence theorem Fixed point Banach space |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001020 |
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