Application of iterative processes of R-order at least three to operators with unbounded second derivative.

  1. Hernández, M.A. 1
  2. Romero, N. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Applied Mathematics and Computation

ISSN: 0096-3003

Año de publicación: 2007

Volumen: 185

Número: 1

Páginas: 737-747

Tipo: Artículo

DOI: 10.1016/J.AMC.2006.07.081 SCOPUS: 2-s2.0-33846894716 WoS: WOS:000244987700071 GOOGLE SCHOLAR

Otras publicaciones en: Applied Mathematics and Computation

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Resumen

In this paper, we apply a family of Newton-like methods, which contains the best known iterative processes, to operator equations where the usual convergence conditions are relaxed. We weaken these conditions by assuming ∥F″(x0)∥ ≤ α and ∥F″(x) - F″(y)∥ ≤ ω(∥x - y∥), with ω a non-decreasing continuous real function. Our results include the ones obtained when the convergence of the family is studied under Lipschitz continuous or Hölder continuous conditions for the second derivative of the operator involved. To finish, we apply the study to boundary value problems. © 2006 Elsevier Inc. All rights reserved.