English

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

Classical Analysis and ODEs 2024-07-08 v1 Numerical Analysis Numerical Analysis

Abstract

This article aims to present the ATAT 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 ATAT 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 SS, normal-SS, Varat, Mann, Ishikawa, FF^{*} , and Picard algorithms. Additionally, the study explores the ATAT algorithm's almost stable behavior for weak contractions. Emphasizing practical applicability, the paper offers data-dependent results through the ATAT algorithm and substantiates findings with illustrative numerical examples

Keywords

Cite

@article{arxiv.2407.03337,
  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}
}

Comments

17 pages, 2 figure

R2 v1 2026-06-28T17:28:18.295Z