On the local convergence of a Newton-type method in Banach spaces under a gamma—type condition

• Argyros, Ioannis K. ^[1] ; Hilout, Saïd ^[2]
  1. [1] Cameron University

     Cameron University

     Estados Unidos

     
  2. [2] Poitiers University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 27, Nº. 1, 2008, págs. 1-14
• Idioma: inglés
• DOI: 10.4067/S0716-09172008000100001
• Enlaces
  • Texto completo
• Resumen

  • We provide a local convergence analysis for a Newton-type method to approximate a locally unique solution of an operator equation in Banach spaces. The local convergence of this method was studied in the elegant work by Werner in [11], using information on the domain of the operator. Here, we use information only at a point and a gamma-type condition [4], [10]. It turns out that our radius of convergence is larger, and more general than the corresponding one in [10]. More over the same can hold true when our radius is compared with the ones given in [9] and [11]. A numerical example is also provided.

• Referencias bibliográficas
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