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Proyecciones (Antofagasta)

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Abstract

ARGYROS, IOANNIS K  and  HILOUT, SAÏD. ON THE LOCAL CONVERGENCE OF A TWO-STEP STEFFENSEN-TYPE METHOD FOR SOLVING GENERALIZED EQUATIONS. Proyecciones (Antofagasta) [online]. 2008, vol.27, n.3, pp.319­-330. ISSN 0716-0917.  http://dx.doi.org/10.4067/S0716-09172008000300007.

We use a two-step Steffensen-type method [1], [2], [4], [6], [13]-[16] to solve a generalized equation in a Banach space setting under Hölder-type conditions introduced by us in [2], [6] for nonlinear equations. Using some ideas given in [4], [6] for nonlinear equations, we provide a local convergence analysis with the following advantages over related [13]-[16]: finer error bounds on the distances involved, and a larger radius of convergence. An application is also provided.

Keywords : Banach space; Steffensen’s method; generalized equation; Aubin continuity; Hölder continuity; radius of convergence; divided difference; set- valued map.

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