ON THE APPROXIMATE SOLUTION OF IMPLICIT FUNCTIONS USING THE STEFFENSEN METHOD

are continuous.The importance of studying inexact Steffensen-Aitken methodscomes from the fact that many commonly used variants can be con-sidered procedures of this type. Indeed approximation (2) character-izes any iterative process in which corrections are taken as approxi-mate solutions of Steffensen-Aitken equations. Moreover we note thatif for example an equation on the real line is solved