Enhancing the applicability of Jarratt-type fourth-order and sixth-order iterative methods

Abstract

In this paper, we extended the applicability of the convergence analysis of the sixth-order iterative methods for solving nonlinear equations studied by Yaseen and Zafar (Arab J Math 11:585-599, 2022), whose analysis uses derivatives up to order seven. Also, we have done convergence analysis for the fourth-order method which can be obtained from their method by considering first two steps. Our analysis is applicable in more general Banach space settings and uses only the first three Frechet derivatives of the involved operator with Lipschitz-type conditions. Also, our analysis gives the computable radius of the convergence ball and the number of iterations to obtain the solution with a given accuracy. © The Author(s) 2025.