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.
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.


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.

Biografía del autor

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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Cómo citar
Argyros, I., & Hilout, S. (2017). On the local convergence of a two-step steffensen-type method for solving generalized equations. Proyecciones. Revista De Matemática, 27(3), 319-330. https://doi.org/10.4067/S0716-09172008000300007