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

2024/05/14 by Akansha Tyagi, Tyagi, Akansha, Sachin Vashistha +1
Mathematics · #Advanced Optimization Algorithms Research

paper · pdf · doi:10.48550/arxiv.2407.03337

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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