Four-Step <i>T</i>-Stable Generalized Iterative Technique with Improved Convergence and Various Applications
This research presents a new form of iterative technique for Garcia-Falset mapping that outperforms previous iterative methods for contraction mappings. We illustrate this fact through comparison and present the findings graphically. The research also investigates convergence of the new iteration in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/14/1/71 |
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| _version_ | 1832589143836721152 |
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| author | Quanita Kiran Shaista Begum |
| author_facet | Quanita Kiran Shaista Begum |
| author_sort | Quanita Kiran |
| collection | DOAJ |
| description | This research presents a new form of iterative technique for Garcia-Falset mapping that outperforms previous iterative methods for contraction mappings. We illustrate this fact through comparison and present the findings graphically. The research also investigates convergence of the new iteration in uniformly convex Banach space and explores its stability. To further support our findings, we present its working on to a BV problem and to a delay DE. Finally, we propose a design of an implicit neural network that can be considered as an extension of a traditional feed forward network. |
| format | Article |
| id | doaj-art-c5fbc3cf6154469fb43d4d1bc148d3f3 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-c5fbc3cf6154469fb43d4d1bc148d3f32025-01-24T13:22:20ZengMDPI AGAxioms2075-16802025-01-011417110.3390/axioms14010071Four-Step <i>T</i>-Stable Generalized Iterative Technique with Improved Convergence and Various ApplicationsQuanita Kiran0Shaista Begum1School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Sector H-12, Islamabad 44000, PakistanSchool of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad 44000, PakistanThis research presents a new form of iterative technique for Garcia-Falset mapping that outperforms previous iterative methods for contraction mappings. We illustrate this fact through comparison and present the findings graphically. The research also investigates convergence of the new iteration in uniformly convex Banach space and explores its stability. To further support our findings, we present its working on to a BV problem and to a delay DE. Finally, we propose a design of an implicit neural network that can be considered as an extension of a traditional feed forward network.https://www.mdpi.com/2075-1680/14/1/71Garcia-Falsetstabilityiterative methodsimplicit neural networkdelay differential equationsboundary value problems |
| spellingShingle | Quanita Kiran Shaista Begum Four-Step <i>T</i>-Stable Generalized Iterative Technique with Improved Convergence and Various Applications Axioms Garcia-Falset stability iterative methods implicit neural network delay differential equations boundary value problems |
| title | Four-Step <i>T</i>-Stable Generalized Iterative Technique with Improved Convergence and Various Applications |
| title_full | Four-Step <i>T</i>-Stable Generalized Iterative Technique with Improved Convergence and Various Applications |
| title_fullStr | Four-Step <i>T</i>-Stable Generalized Iterative Technique with Improved Convergence and Various Applications |
| title_full_unstemmed | Four-Step <i>T</i>-Stable Generalized Iterative Technique with Improved Convergence and Various Applications |
| title_short | Four-Step <i>T</i>-Stable Generalized Iterative Technique with Improved Convergence and Various Applications |
| title_sort | four step i t i stable generalized iterative technique with improved convergence and various applications |
| topic | Garcia-Falset stability iterative methods implicit neural network delay differential equations boundary value problems |
| url | https://www.mdpi.com/2075-1680/14/1/71 |
| work_keys_str_mv | AT quanitakiran fourstepitistablegeneralizediterativetechniquewithimprovedconvergenceandvariousapplications AT shaistabegum fourstepitistablegeneralizediterativetechniquewithimprovedconvergenceandvariousapplications |