The Impact of Data Dependence, Convergence and Stability by $AT$ Iterative Algorithms
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917712795533312 |
|---|---|
| author | Tyagi, Akansha Vashistha, Sachin |
| author_facet | Tyagi, Akansha Vashistha, Sachin |
| contents | This article aims to present the $AT$ algorithm, a novel two-step iterative approach for approximating fixed points of weak contractions within complete normed linear spaces. The article demonstrates the convergence of $AT$ algorithm towards fixed points of weak contractions. Notably, it establishes the algorithm's strong convergence properties, highlighting its faster convergence compared to established iterative methods such as $S$, normal-$S$, Varat, Mann, Ishikawa, $F^{*} $, and Picard algorithms. Additionally, the study explores the $AT$ algorithm's almost stable behavior for weak contractions. Emphasizing practical applicability, the paper offers data-dependent results through the $AT$ algorithm and substantiates findings with illustrative numerical examples |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03337 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Impact of Data Dependence, Convergence and Stability by $AT$ Iterative Algorithms Tyagi, Akansha Vashistha, Sachin Classical Analysis and ODEs Numerical Analysis This article aims to present the $AT$ algorithm, a novel two-step iterative approach for approximating fixed points of weak contractions within complete normed linear spaces. The article demonstrates the convergence of $AT$ algorithm towards fixed points of weak contractions. Notably, it establishes the algorithm's strong convergence properties, highlighting its faster convergence compared to established iterative methods such as $S$, normal-$S$, Varat, Mann, Ishikawa, $F^{*} $, and Picard algorithms. Additionally, the study explores the $AT$ algorithm's almost stable behavior for weak contractions. Emphasizing practical applicability, the paper offers data-dependent results through the $AT$ algorithm and substantiates findings with illustrative numerical examples |
| title | The Impact of Data Dependence, Convergence and Stability by $AT$ Iterative Algorithms |
| topic | Classical Analysis and ODEs Numerical Analysis |
| url | https://arxiv.org/abs/2407.03337 |