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


  • Ioannis K. Argyros Cameron university.
  • Saïd Hilout Université Sultan Moulay Slimane.




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.


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.

Author Biographies

Ioannis K. Argyros, Cameron university.

Department of Mathematics Sciences.

Saïd Hilout, Université Sultan Moulay Slimane.

Faculty of Science & Technics of Béni-Mellal. Department of Applied Mathematics & Computation.


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How to Cite

I. K. Argyros and S. Hilout, “On the local convergence of a two-step steffensen-type method for solving generalized equations”, Proyecciones (Antofagasta, On line), vol. 27, no. 3, pp. 319-330, Apr. 2017.




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