On improving the applicability of some higher-order iterative processes

In this paper, two-step and three-step iterative processes with generic parameters are considered, and their semi-local convergence analysis (SLCA) and local convergence analysis (LCA) are presented. Further, the considered class of iterative processes contains some of the existing iterative processes of order four, five, seven, and eight, whose convergence analysis uses the derivative of the involved operator up to order five, six, eight and nine, respectively, to get the order of convergence (OC). However, we need the derivatives up to order two only to get the OC in our analysis, which is provided in Banach space settings. We also compute the radius of the convergence ball and the number of iterations to reach the solution with a tolerance are also obtained. The basin of attraction for the considered iterative processes is illustrated through an example to demonstrate the performance of these processes.