ON THE LOCAL CONVERGENCE OF A NEWTON—TYPE METHOD IN BANACH SPACES UNDER A GAMMA—TYPE CONDITION

We provide a local convergence analysis for a Newton—type method to approximate a locally unique solution of an operator equation in Ba-nach 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. AMS Subject Classification. 65G99, 65K10, 47H17, 49M15