Analysis of the Convergence Behaviour of Double-Step and Triple-Step Iteration Schemes

Abstract

Fixed point iterative methods are commonly used to solve equations arising from physical models. However, a comprehensive numerical analysis of these methods is often lacking. In this work, we provide a rigorous analysis of the convergence behavior and associated rates of convergence of selected iterative approaches under variational conditions in Banach space with the aid of Z-operator. Furthermore, the study examines the existence of fixed points generated by the S-iteration and Noor iterative schemes.