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arXiv · 2407.03337

The Impact of Data Dependence, Convergence and Stability by $AT$ Iterative Algorithms

Akansha Tyagi·Sachin Vashistha
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Abstract

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

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Akansha Tyagi, Sachin Vashistha. 2024-05-14. The Impact of Data Dependence, Convergence and Stability by $AT$ Iterative Algorithms. https://arxiv.org/abs/2407.03337

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