TY - JOUR AU - Argyros, Ioannis K. AU - Hilout, Saïd PY - 2017/05/02 Y2 - 2024/03/28 TI - On the local convergence of a Newton-type method in Banach spaces under a gamma—type condition JF - Proyecciones (Antofagasta, On line) JA - Proyecciones (Antofagasta, On line) VL - 27 IS - 1 SE - DO - 10.4067/S0716-09172008000100001 UR - https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1524 SP - 1-14 AB - <span class="fontstyle0">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.<br /></span> ER -