On the local convergence of a two-step steffensen-type method for solving generalized equations

Ioannis K. Argyros, Saïd Hilout


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.

Palabras clave

Banach space; Steffensen’s method; generalized equation; Aubin continuity; Hölder continuity; radius of convergence; divided difference; set—valued map; espacio de Banach; método de Steffensen; ecuación generalizada; continuidad de Aubin.

Texto completo:



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DOI: http://dx.doi.org/10.4067/S0716-09172008000300007

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