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

  • Ioannis K. Argyros Cameron University.
  • Saïd Hilout Poitiers University.
Palabras clave: Banach space, Newton—type method, local convergence, gamma—type condition, Frechet—derivative, radius of convergence, espacio de Banach, método tipo Newton, convergencia local, condiciones tipo gamma, derivada de Frechet, radio de convergencia.


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.

Biografía del autor

Ioannis K. Argyros, Cameron University.
Department of Mathematics Sciences.
Saïd Hilout, Poitiers University.
Laboratoire de Mathématiques et Applications.


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Cómo citar
Argyros, I., & Hilout, S. (2017). On the local convergence of a Newton-type method in Banach spaces under a gamma—type condition. Proyecciones. Journal of Mathematics, 27(1), 1-14. https://doi.org/10.4067/S0716-09172008000100001