# 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.

### 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.

### Biografía del autor

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

### Citas

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