TY - JOUR
AU - Ioannis Argyros
AU - Saïd Hilout
PY - 2017/05/02
Y2 - 2019/02/19
TI - On the local convergence of a Newton-type method in Banach spaces under a gamma—type condition
JF - Proyecciones. Revista de Matemática
JA - PJM
VL - 27
IS - 1
SE - Artículos
DO - 10.4067/S0716-09172008000100001
UR - http://www.revistaproyecciones.cl/article/view/1524
AB - 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.
ER -