{
  "id": "2407.03337",
  "version": "v1",
  "published": "2024-05-14T11:51:13.000Z",
  "updated": "2024-05-14T11:51:13.000Z",
  "title": "The Impact of Data Dependence, Convergence and Stability by $AT$ Iterative Algorithms",
  "authors": [
    "Akansha Tyagi",
    "Sachin Vashistha"
  ],
  "comment": "17 pages, 2 figure",
  "categories": [
    "math.CA",
    "cs.NA",
    "math.NA"
  ],
  "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",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-14T11:51:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "data dependence",
      "iterative algorithms",
      "weak contractions",
      "paper offers data-dependent results",
      "algorithms strong convergence properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}