The Impact of Data Dependence, Convergence and Stability by $AT$ Iterative Algorithms
<|reference_start|>The Impact of Data Dependence, Convergence and Stability by $AT$ Iterative Algorithms: 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<|reference_end|>
@article{tyagi2024the,
    title={The Impact of Data Dependence, Convergence and Stability by $AT$
  Iterative Algorithms},
    author={Akansha Tyagi and Sachin Vashistha},
    journal={arXiv preprint arXiv:2407.03337},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.03337},
    primaryClass={math.CA cs.NA math.NA}
}