A class of generalized Newton iterative schemes Original Research Article

We study an N-step iterative scheme which generalizes several Newton-type schemes that have appeared in the literature. We show that, under generalized Zabrejko-Nguen conditions, the iterative scheme converges whenever 1 ≤ N ≤ ∞. This proves in a unified context the convergence of an infinite number of iterative schemes which include as special cases the classical Newton scheme, the classical chord scheme, and the generalized Newton scheme.