Some Newton-like methods with sharper error estimates for solving operator equations in Banach spaces

摘要

It is well known that the rate of convergence of S-iteration process introduced by Agarwal et al. (pp. 61-79) is faster than Picard iteration process for contraction operators. Following the ideas of S-iteration process, we introduce some Newton-like algorithms to solve the non-linear operator equation in Banach space setting. We study the semi-local as well as local convergence analysis of our algorithms. The rate of convergence of our algorithms are faster than the modified Newton method. Mathematics Subject Classification 2010: 49M15; 65K10; 47H10.