Resumen de On Steffensen�s method on Banach spaces

José Antonio Ezquerro Fernández , Miguel Angel Hernández Verón , Natalia Romero Álvarez , A. I. Velasco

• We present a modification of Steffensen�s method as a predictor�corrector iterative method, so that we can use Steffensen�s method to approximate a solution of a nonlinear equation in Banach spaces from the same starting points from which Newton�s method converges.Westudy the semilocal convergence of the predictor�corrector method by using the majorant principle.Weillustrate the method with an application to a discrete problem.