Abstract
We develop a class of Steffensen-like schemes for approximating solution of Banach space valued equations. The sequences generated by these schemes are, converging to the solution under certain hypotheses that are weaker than in earlier studies. Hence, extending the region of applicability of these schemes without additional hypotheses. Benefits include: more choices for initial points; the computation of fewer iterates to reach a certain accuracy in the error distances, and a more precise knowledge of the solution. Technique is applicable on other schemes our due to its generality.