Resumen

ARGYROS, Ioannis K. ON THE LOCAL CONVERGENCE OF A MIDPOINT METHOD IN BANACH SPACES UNDER A GAMMA-TYPE CONDITION. Proyecciones (Antofagasta) [online]. 2009, vol.28, n.2, pp. 155-167. ISSN 0716-0917.  doi: 10.4067/S0716-09172009000200005.

In this study we are concerned with the problem of approximating a locally unique solution of an operator equation in a Banach space setting using the midpoint method, introduced by us in [5], [6]. Here, we use gamma-type condition to provide a local convergence analysis. Our results compare favorably with the relevant ones in [9], [11], [12]-[14]- In particular our radius of convergence is larger. Numerical examples are also provided.

Palabras clave : Midpoint method; Banach space; Gamma-type condition; radius of convergence; local convergence; Fréchet-derivative.