A class of generalized Newton iterative schemes (Q1431899)

The author studies an \(N\)-step iterative scheme which generalizes several Newton-type schemes that have appeared in the literature. He shows that, under generalized Zabrejko-Nguen conditions, the iterative scheme converges whenever \(1\leq N\leq\infty\). 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 as has been considered before, e.g., by \textit{E. de Pascale}, \textit{J. V. Lysenko}, \textit{P. P. Zabrejko} and the reviewer [Numer. Funct. Anal. Optimization 18, No. 1--2, 1--17 (1997; Zbl 0881.65048)].