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

Ioannis K. Argyros, Saïd Hilout


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.

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.

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DOI: http://dx.doi.org/10.4067/S0716-09172008000100001

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