A two-step Steffensen's method under modified convergence conditions

A simplification of a third order iterative method is proposed. The main advantage of this method is that it does not need to evaluate neither any Fréchet derivative nor any bilinear operator. A semilocal convergence theorem in Banach spaces, under modified Kantorovich conditions, is analyzed. A local convergence analysis is also performed. Finally, some numerical results are presented.